Stereoscopic sheet structure

ABSTRACT

An object of the present invention is to provide a stereoscopic sheet structure in which a three-dimensional design appears to be changing by changing the angle of observation, the stereoscopic sheet structure being a stereoscopic sheet structure that has: a convex lens assembly which is formed on one surface of a sheet member and in which a plurality of convex lenses are arranged; and a repeating design portion in which a plurality of design units are arranged on a focal plane of the convex lenses at arrangement intervals and/or in arrangement directions different from those of the convex lenses, and which has a continuously deformed design portion in which the arrangement intervals and arrangement directions of the design units regularly change while satisfying the condition of 0.95≦D N˜N+1 /D N+1˜N+2 ≦0.95 and −1≦θ≦+1. It should be noted that the D is an interval between adjacent design elements, and the θ is an intersection angle that is formed between a straight line connecting adjacent design elements and a straight line connecting one of the adjacent design elements to a design element adjacent thereto.

TECHNICAL FIELD

The present invention relates to a stereoscopic sheet structure and,more particularly, to a stereoscopic sheet structure in whichthree-dimensional moiré designs appear as though, for example, the shapeof design units forming the three-dimensional moiré designs, the size ofthe design units, the positions of the design units, and/or spacesbetween the design units were changed by changing the angle ofobservation.

BACKGROUND ART

Patent Document 1 has an object of “providing a decorative sheet inwhich three-dimensional designs are formed on a transparent sheet byforming pattern portions on the front and rear surfaces of thetransparent sheet,” and proposes “a decorative sheet characterized inthat one side of the transparent sheet is provided with a first patternportion having first designs that are repeatedly formed at predeterminedintervals, and the other side of the transparent sheet is provided witha second pattern portion having moiré designs that are formed by seconddesigns having a similar shape as that of the first designs” (see claim1 and the paragraph 0005 of Patent Document 1). Patent Document 2 has anobject of “providing a decorative sheet in which three-dimensionallydeveloped designs are changed,” and proposes “a decorative sheet inwhich designs are developed three-dimensionally by a lens part having aplurality of convex lens-like projections and a design part havingdesigns, wherein the plurality of convex lens-like projections areprovided so as to be changed” (see claim 1 and the paragraph 0005 ofPatent Document 2). Patent Document 3 has an object of “providing, bymeans of an easy and low-cost technique, a sheet that has such anexcellent decorativeness that a design thereof is changeable with theangle of observation,” and proposes “a decorative sheet characterized inthat a plurality of convex lens-shaped projections 21 are provided on afront surface 2 of a transparent sheet 1 in an arbitrary continuouspattern, and designs 31 having the same continuous pattern as the frontsurface 2 are printed on a rear surface 3 of the sheet 1 in displacementfrom the continuous pattern on the front surface 2” (see claim 1 and theparagraph 0004 of Patent Document 3). Patent Document 4 intends to solvethe technical problem in which “a plastic film needs to be embossed tochange its shape and size in order to obtain three-dimensional andenlarged stipple designs having different sizes, and such a processrequires a change of the mold itself, which is expensive, thus it wasdifficult to obtain a variety of enlarged three-dimensional stippledesigns,” and thus proposes “a decorative body with stipple designs, inwhich a number of independent colored or non-colored projectedconverging devices A having transparency are printed, in a regularlyarranged state at certain fine intervals, on a front surface of acolored or non-colored transparent substrate B by means of print inkhaving transparency, and a plurality of colored pixels C having theshape that is the same as or different from that of the projectedconverging devices A formed on the front surface are printed on a rearsurface of the transparent substrate B, in the same arrangement state asthat of the projected converging device A, and further each of thecolored pixels C is positioned by shifting an intersection angle withrespect to each of the projected converging devices A formed on thefront surface so that the size in which the colored pixels C areobserved are changed significantly due to the intersection angle,wherein the colored pixel C appears as an expanded image having athree-dimensional effect when viewed from the front surface, and theexpanded image presents a fluctuation effect when viewed from adifferent perspective” (see claim 1 and the paragraph 0006 of PatentDocument 4).

Moreover, Patent Document 5 has an object of “providing a virtual imageappearing decorative body that causes an expanded virtual image of thesame shape as that of a picture element to appear above or below a planeconvex lens-shaped light collecting element layer,” and discloses “meansof solution, in which a plane convex lens-shaped light collectingelement layer in which a number of plane convex lens-shaped lightcollecting elements of the same shape and size are arranged verticallyand horizontally, and a picture element layer in which a number ofpicture elements of the same shape and size as a transparent substratelayer are arranged vertically and horizontally are configured, whereinat least one pair of the plane convex lens-shaped light collectingelement and the picture element completely overlap with each othervertically, the plane convex lens-shaped light collecting element layerand the picture element layer are arranged so that other pictureelements that are separated at equal distance from the overlappingpicture element are dislocated in the same width toward the outside (orinside) radially around the overlapping picture element to the planeconvex lens-shaped light collecting element facing the abovementionedother picture elements, to increase the dislocation width of the pictureelements from the central picture element toward the outside pictureelements, so that an expanded virtual image of the same shape as theshape of the picture elements is caused to appear above (or below) thelight collecting element layer” (see the abstract of Patent Document 5).Patent Document 6 has an object of “providing a virtual image developingdecorator in which a depth position and a height position from a frontof the decorator of a virtual image are changed in association with analteration made when a direction for visually observing the virtualimage developing decorator is altered,” and discloses means in which“virtual image developing decorator comprises a plano-convex lens-likeconverging element layer formed by laterally and longitudinally aligningmany plano-convex lens-like converging elements, a transparent baseplate layer, and a pixel layer formed by laterally and longitudinallyaligning many pixels at different intervals, so that alignments of onepixels and alignments of another pixels at equal distances to those ofthe one pixels of the alignments of the two perpendicular pixelsincluding the superposed pixels are deviated toward an inside to thealignments of the plano-convex lens-like converting elements, largelydeviated in width at outer side, the alignments of the other pixels andthe alignments of the another pixels at the equal distance to those ofthe one pixels are deviated toward an outside to the alignments of theplano-convex lens-like converging elements, largely deviated in width atthe outer side and the virtual image is developed at the pixelssuperposed above or below the plano-convex lens-like converting elementsas a center according to the direction for visually observing the image”(see the abstract of Patent Document 6). Patent Document 7 has an objectof “providing a decorative body presenting virtual images which presentsenlarged virtual images of pixels above or below aplano-convex-lens-shaped condenser element layer,” and discloses, as themeans for solving the problem, “the decorative body is constituted ofthe plano-convex-lens-shaped condenser element layer formed by lining uplongitudinally and laterally a large number of plano-convex-lens-shapedcondenser elements, a transparent base layer and a pixel layer formed bylining up longitudinally and laterally a large number of pixels. Thesize of each pixel becomes smaller as the pixel is disposed on anotherpixel line located farther from one pixel line selected as a basic pixelline. The plano-convex-lens-shaped condenser element layer and the pixellayer are disposed so that at least one set of the elements overlapsvertically in the most degree, that the other pixels at an equaldistance from the overlapping pixels slip radially from the condenserelements corresponding to the other pixels, with respect to theoverlapping pixel as the center, and that the width of slippage becomeslarger as the pixels are located farther outside from the pixel beingthe center. The enlarged virtual images are presented above or below theplano-convex-lens-shaped condenser element layer” (see the abstract ofPatent Document 7). Patent Document 8 has an object of “providing avirtual image developing decorative object for developing a virtualimage, which is moved in matching relation to respective pixels when avisual position is moved, above or below a planoconcave lens-likecondenser element layer,” and discloses, as the means for solving theproblem, means in which “a plane convex lens light condensing elementlayer in which a plane convex lens light condensing elements arearranged and a pixel layer in which pixels are arranged are provided,wherein the pixels arranged on each pixel row (or each pixel column) ofthe pixel layer are rotated in a pattern accumulating the samerotational angle, a pair of each plane convex lens light condensingelement and each pixel is stacked, a pair of other pixel column that areequally distant from the pixel column having stacked pixels are shiftedfrom the pixel column having stacked pixels toward the outside (or theinside) with respect to the corresponding plane convex lens lightcondensing element column, the plane convex lens light condensingelement layer and the pixel layer are disposed such that the width bywhich the pixel column is shifted becomes large toward the outside ofthe pixel column having stacked pixels, and a virtual image formed above(or below) the plane convex lens light condensing element layer is movedaccording to each pixel when the position of observation is moved” (seethe abstract of Patent Document 8). Patent Document 9 has an object ofproviding “a decorative display on which an enlarged image of astereoscopic figure can be visualized in the static state of littleswaying without restrictions for spots for visualizing,” and discloses,as the means for solving the problem, “a plurality of colored pixels 42provided with the arranging properties and direction properties ofrespective pixels 42 disposed two-dimensionally and at the equalintervals on the back of a sheet-shaped material 41 to form imagepatterns on the decorative display. A plurality of convex lens-shapedbeam condensing elements 44 provided with the direction properties sameas those of the image patterns are formed on lines of respective beamcondensing elements 44 and disposed two-dimensionally to form beamcondensing patterns on the surface of the sheet-shaped transparentmaterial 41. Image patterns 43 and beam condensing patterns are soformed as to provide the disposition pitch of respective pixels 42different from the disposition pitch of respective beam condensingelements 44” (see the abstract of Patent Document 9). Patent Document 10has an object of providing “a decorative display on which thethree-dimensional enlarged image of a pattern appears in a shake-freestatic state wherever it may seen from”, and discloses, as the means forsolving the problem, “in this decorative display, a plurality of coloredpixels 42 are two-dimensionally and evenly arranged on the back side ofa sheet-type transparent material 41, each line of the pixels 42 beinggiven a directivity, to form an image pattern. A plurality of convexlight-condensing elements 44 are also two-dimensionally and evenlyarranged on the front side of the transparent material 41, each line ofthe light-condensing elements 44 being given the same directivity asthat of the image pattern, to form a light-condensing element pattern.The image pattern 43 and the light-condensing element pattern are formedin a way that the pixels 42 and the light-condensing elements 44 differin array pitch” (see the abstract of Patent Document 10).

[Patent Document 1] Japanese Patent No. 3131771 [Patent Document 2]Japanese Published Unexamined Patent Application No. 2003-39583 [PatentDocument 3] Japanese Patent No. 2761861 [Patent Document 4] JapanesePatent No. 3338860 [Patent Document 5] Japanese Published UnexaminedPatent Application No. 2001-55000 [Patent Document 6] Japanese PublishedUnexamined Patent Application No. 2002-46400 [Patent Document 7]Japanese Published Unexamined Patent Application No. 2002-120500 [PatentDocument 8] Japanese Published Unexamined Patent Application No.2003-226099 [Patent Document 9] Japanese Published Unexamined PatentApplication No. 2001-180198 [Patent Document 10] Japanese PublishedUnexamined Patent Application No. 2003-220173 DISCLOSURE OF THEINVENTION Problems to be Solved by the Invention

However, these stereoscopic sheet structures and the like have thefollowing problems; even if the designs are observed at different anglesvia the lens assembly, the degree of the displacement of the positionsat which the designs appear is constant and the designs appear simplythree-dimensionally, thus a three-dimensional visual effect is small.Besides, the shapes of the three-dimensional designs are not changed,thus, again, a three-dimensional visual effect is small. Moreover, inthese stereoscopic sheet structures and the like where the designsappear as though they are displaced, depending on the angle at which thedesigns are observed, the amount of displacement of the designs becomessmall when the distance of observing the stereoscopic sheet structurebecomes longer (when visual distance becomes longer), and as a resultthe effect of viewing the designs three-dimensionally becomes small.

Means to Solve the Problems

Therefore, it is an object of the present invention to provide astereoscopic sheet structure in which three-dimensional moiré designsappear variably by changing the angle of observation when the designsare observed via a lens assembly. More specifically, an object of thepresent invention is to provide a stereoscopic sheet structure in whichwhen three-dimensional moiré designs are observed via a lens assembly,the designs appear as though they were displaced and moved, by changingthe angle of observation, even if the visual distance is long or short,and a stereoscopic sheet structure in which the shape of thethree-dimensional moiré designs appears variably by changing the angleof observation.

As first means for achieving the abovementioned object, claim 1 isdirected to a stereoscopic sheet structure, comprising:

a convex lens assembly which is provided on one surface of a sheetmember and in which a plurality of convex lenses for focusing light onthe other surface are disposed at predetermined arrangement intervalsand in predetermined arrangement directions; and

a repeating design portion in which a plurality of design units arearranged on a focal plane of the convex lenses at arrangement intervalsand/or in arrangement directions different from those of the convexlenses, and which has a continuously deformed design portion in whichthe arrangement intervals of the design units change regularly such thatwhen any three adjacent design units are selected, a ratio(D_(N˜N+1)/D_(N+1˜N+2)) of an interval L_(N˜N+1) between a N^(th) designunit N and a N+1^(th) design unit N+1 adjacent thereto to an intervalD_(N+1˜N+2) between the N+1^(th) design unit N+1 and a N+2^(th) designunit N+2 adjacent thereto falls within a range of 0.95 to 1.05, and thearrangement directions of the design units change regularly such that anintersection angle that is formed between an extended line of a straightline connecting the N^(th) design unit N and the N+1^(th) design unitN+1 adjacent thereto and a straight line connecting the N+1^(th) designunit N+1 and the N+2^(th) design unit N+2 adjacent thereto falls withina range of −1 degree to +1 degree.

As second means for achieving the abovementioned object, claim 4 isdirected to a stereoscopic sheet structure, comprising:

a convex lens assembly which is provided on one surface of a sheetmember and in which a plurality of convex lenses for focusing light onthe other surface are disposed at predetermined arrangement intervalsand in predetermined arrangement directions; and

a repeating design portion in which a plurality of design units arearranged on a focal plane of the convex lenses at arrangement intervalsand/or in arrangement directions different from those of the convexlenses, and which has a line segment assembly portion in which thedesign units are line segments, and the plurality of line segments arearranged at intervals different from the arrangement intervals of theconvex lenses of the convex lens assembly.

In a preferred embodiment of the stereoscopic sheet structure, therepeating design portion has a plurality of the line segment assemblyportions, and directions of extension of the plurality of line segmentsforming one of the line segment assembly portions are different fromdirections of extension of the line segments forming other line segmentassembly portions.

As third means for achieving the abovementioned object, claim 2 isdirected to a stereoscopic sheet structure, comprising:

a convex lens assembly which is provided on one surface of a sheetmember and in which a plurality of convex lenses for focusing light onthe other surface are disposed at predetermined arrangement intervalsand in predetermined arrangement directions; and

a repeating design portion in which a plurality of design units arearranged on a focal plane of the convex lenses at arrangement intervalsand/or in arrangement directions different from those of the convexlenses, and which has a continuously deformed design portion in which adesign pattern that has the plurality of design units arranged atarrangement intervals different from the arrangement intervals of theplurality of convex lenses of the convex lens assembly has formedtherein a plurality of sections obtained by division at regularintervals in the respective arrangement directions of the design unitsand have the equal number of design units, and the design pattern isdeformed such that the section formed along at least one of thearrangement directions has a plurality of design units that are arrangedin the one direction at arrangement intervals different from anarrangement intervals that follow the one direction in the design unitscontained in another section adjacent to the section in the onedirection.

As fourth means for achieving the abovementioned object, claim 3 isdirected to the stereoscopic sheet structure according to claim 1 or 2,comprising:

a convex lens assembly which is provided on one surface of a sheetmember and in which a plurality of convex lenses for focusing light onthe other surface are disposed at predetermined arrangement intervalsand in predetermined arrangement directions; and

a repeating design portion in which a plurality of design units arearranged on a focal plane of the convex lenses at arrangement intervalsand/or in arrangement directions different from those of the convexlenses, and which has the continuously deformed design portion describedin claim 1 and the continuously deformed design portion described inclaim 2.

As fifth means for achieving the abovementioned object, claim 6 is thestereoscopic sheet structure according to any of claims 1 through 5,comprising:

the convex lens assembly of claim 1 on one surface of a first sheetmember; and

the repeating design portion of any one of claims 1 through 5 on onesurface of a second sheet member,

wherein the first sheet member and the second sheet member are stackeddetachably or integrally so that a focal plane of the convex lenses ofthe first sheet member faces the surface of the second sheet member thathas the repeating design portion.

According to the present invention, a stereoscopic sheet structure inwhich three-dimensional moiré designs appear variably by changing theangle of observation can be provided.

Specifically, the present invention, particularly the stereoscopic sheetstructures described in claim 1 and claim 4, can provide a stereoscopicsheet structure in which when the three-dimensional moiré designs areobserved via the lens assembly, the three-dimensional moiré designsappear as though they were displaced and moved, by changing the angle ofobservation, even if the visual distance is long or short.

Therefore, the present invention can sufficiently fulfill a function inwhich the three-dimensional moiré designs appear as though they weredisplaced and moved, by changing the angle of observation, thus thestereoscopic sheet structure of the present invention can be applied toan advertising display in the street, a poster, an advertisement tower,an information display board and the like that can be observed at a longvisual distance, in addition to a packaging material and the like thatare normally observed at a short visual distance.

Moreover, the present invention, particularly the stereoscopic sheetstructure described in claim 2, can provide a stereoscopic sheetstructure in which when the three-dimensional moiré designs are observedvia the lens assembly, the shape of the designs appears variably bychanging the angle of observation. Therefore, the present invention canfulfill a function in which the shape of the three-dimensional moirédesigns appears variably by changing the angle of observation, thus thestereoscopic sheet structure of the present invention can be appliedsuitably to a packaging material, an advertising display in the street,a poster, an advertisement tower, an information display board and thelike that catch the eye.

In addition, the present invention has the continuously deformed designportion in which a part or the whole of the repeating designs isdeformed, and the line segment assembly portion, and the continuouslydeformed design portion and the line segment assembly portion can beformed easily, thus the stereoscopic sheet structure having theabovementioned effects can be produced easily.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view showing the stereoscopicsheet structure as an example of the present invention.

FIG. 2 is a view showing an example of an arrangement that can beadopted as the arrangement of a convex lens assembly.

FIG. 3 is a view showing an example of an arrangement that can beadopted as the arrangement of the convex lens assembly.

FIG. 4 is a view showing an example of an arrangement that can beadopted as the arrangement of the convex lens assembly.

FIG. 5 is a view showing an example of an arrangement that can beadopted as the arrangement of the convex lens assembly.

FIG. 6 is a view showing an example of an arrangement that can beadopted as the arrangement of the convex lens assembly.

FIG. 7 is a view showing an example of an arrangement that can beadopted as the arrangement of the convex lens assembly.

FIG. 8 is a view showing an example of an arrangement that can beadopted as the arrangement of the convex lens assembly.

FIG. 9 is a view showing an example of patterns that can be adopted asdesign patterns.

FIG. 10 is a view showing an example of a continuously deformed designportion in the stereoscopic sheet structure of a first embodiment.

FIG. 11 is a view for explaining a continuously deformed design that isconfigured by continuously changing an arrangement angle θ that isformed between the direction of the arrangement of design units 31formed along an auxiliary line Y₀ of the design patterns shown in FIG. 9and a straight line connecting the two design units 31.

FIG. 12 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the first embodiment.

FIG. 13 is a view for explaining a continuously deformed design that isconfigured by continuously changing an arrangement interval d betweentwo design units 31 that are adjacent in an arrangement directionfollowing the auxiliary line Y₀ in the arrangement of the design units31 formed along the auxiliary line Y₀ of the design patterns shown inFIG. 9.

FIG. 14 is a view showing an example of patterns that can be adopted asdesign patterns.

FIG. 15 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the first embodiment.

FIG. 16 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the first embodiment.

FIG. 17 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the first embodiment.

FIG. 18 is a schematic cross-sectional view showing the stereoscopicsheet structure as an example of the present invention.

FIG. 19 is a schematic cross-sectional view showing the stereoscopicsheet structure as an example of the present invention.

FIG. 20 is a schematic cross-sectional view showing the stereoscopicsheet structure as an example of the present invention.

FIG. 21 is a view showing an example of line segments that can beadopted as line segments configuring a line segment assembly portion ofa stereoscopic sheet structure of a second embodiment in ahoneycomb-shaped arrangement.

FIG. 22 is a view showing an example of line segments that can beadopted as line segments configuring a line segment assembly portion ofthe stereoscopic sheet structure of the second embodiment in asquare-shaped arrangement.

FIG. 23 is a view showing an example of a repeating design in thestereoscopic sheet structure of the second embodiment.

FIG. 24 is a view showing an example of the line segment assemblyportion in the stereoscopic sheet structure of the second embodiment.

FIG. 25 is a schematic cross-sectional view showing the stereoscopicsheet structure as an example of the present invention.

FIG. 26 is a view showing an example of patterns that can be adopted asdesign patterns.

FIG. 27 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of a third embodiment.

FIG. 28 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 29 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 30 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 31 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 32 is a view showing an example of patterns that can be adopted asdesign patterns.

FIG. 33 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 34 is a view showing an example of the continuously deformed designportion in the stereoscopic-sheet structure of the third embodiment.

FIG. 35 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 36 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 37 is a view showing an example of the continuously deformed designportion in the stereoscopic sheet structure of the third embodiment.

FIG. 38 is a schematic view showing a three-dimensional moiré designthat can be observed when a continuously deformed design portion 46 isviewed from the top of a convex lens 21 configuring a convex lensassembly 20.

FIG. 39 is a schematic view showing a three-dimensional moiré designthat can be observed when the angle of observation is moved in ahorizontal direction to view the continuously deformed design portion 46from the top of the convex lens 21 configuring the convex lens assembly20.

EXPLANATION OF REFERENCE NUMERALS

-   -   1, 2, 3, 4, 5 Stereoscopic sheet structure    -   10, 11 Sheet member    -   15 Image    -   20 Convex lens assembly    -   21 Convex lens    -   22 Lens forming section    -   30, 30B, 50, 70 Repeating design    -   31, 32 Design unit    -   35, 36, 37, 38, 39 Design pattern    -   40 through 49A Continuously deformed design portion    -   60 Line segment assembly portion    -   65 Line segment

BEST MODE FOR CARRYING OUT THE INVENTION

A first embodiment of the present invention, that is, a stereoscopicsheet structure 1 which is an example of the stereoscopic sheetstructure described in claim 1 is described with reference to thedrawings. In the stereoscopic sheet structure 1 of the first embodiment,as shown in FIG. 1, one surface of a sheet member 10 has a convex lensassembly 20 having a plurality of convex lenses 21 formed thereon, andthe other surface of the same has a repeating design portion 30.

As shown in FIG. 1, the sheet member 10 is composed of one sheet andsupports the convex lens assembly 20, which is described hereinafter.The stereoscopic sheet structure 1 is so designed as to observe, throughthe convex lens assembly 20, the repeating design portion 30 that isformed on a surface opposite to the one surface of the sheet member 10on which the convex lens assembly 20 is formed, thus it is required thatthe sheet member 10 is transparent. Here, the term “transparent” meansthat the sheet member 10 has sufficient transparency to observe therepeating design portion 30, and includes the concept of transparent andcolorless, half-transparent, and colored and transparent states. Thematerial of the sheet member 10 may be a transparent material so as tobe able to support the convex lens assembly 20, and examples include asynthetic resin, glass, a transparent coating film and the like.

The thickness of the sheet member 10 is substantially the same as thefocal length of the convex lenses 21. In other words, when the convexlens assembly 20 is formed on one of the surfaces of the sheet member10, the thickness of the sheet member 10 is determined such that theconvex lenses 21 of the convex lens assembly 20 focus light on the othersurface of the sheet member 10. The thickness of the sheet member 10 isnormally 0.1 through 10.0 mm according to the focal length of the convexlenses 21, but may be 0.1 through 0.8 mm. The sheet member 10 may have ashape so as to be able to support the convex lens assembly 20 andapplied to an information display board or the like, and can be formedinto a plate having, for example, planar shape, curved shape, or anyconcave or convex shape.

In this sheet member 10, the surface thereof on which theafter-described convex lens assembly 20 is formed is preferably assmooth as possible. Preferred smoothness of the surface of the sheetmember 10 on which the convex lens assembly 20 is formed can be definedby an arithmetic average roughness value (Ra value) defined by JIS B0601 and the maximum height value (Ry value). The Ra value of thesurface of the sheet member 10 on which the convex lens assembly 20 isformed is preferably 0.001 through 5 (μm), and particularly preferably0.002 through 0.6 (μm), and the Ry value is preferably 0.001 through 28(μm), and particularly preferably 0.002 through 3 (μm). It should benoted that in some cases a preferred range of the Ra value can be from0.001 through 0.6 and 0.002 through 5, and a preferred range of the Ryvalue can be from 0.002 through 28 and 0.001 through 3. If thesmoothness of the surface of the sheet member 10 on which the convexlens assembly 20 is formed is within the abovementioned ranges, theconvex lens assembly 20 can be provided with uniform convex lenses 21,and especially the convex lens assembly 20 can be formed effectively bymeans of print processes described hereinafter. If the smoothness of theabovementioned planar surface is poor, eventually the function of theconvex lens assembly 20 to be formed becomes deteriorated.

The convex lens assembly 20 is configured by forming a plurality ofconvex lenses 21 on a surface of the sheet member 10. The convex lenses21 may be arranged so as to be able to obtain a special visual effectwhere the design units of the repeating design portion appear as thoughthey were floating or subducted, and such arrangement is characterizedby a lens forming section in which a single convex lens 21 is formed, aspace between the lens forming sections, and the like. Examples of theshape of the lens forming section include polygons such as triangle,square, pentagon and hexagon, circle, ellipse, and the like. In the lensforming section, a single convex lens 21 is formed, whereby anarrangement of the convex lenses 21 is determined. The size of a patternforming section (a space between adjacent pattern forming sections) isdetermined according to an arrangement interval L of the convex lenses,as described hereinafter.

Examples of the arrangement of the convex lens assembly 20 include thearrangements shown in FIG. 2 through FIG. 8. The arrangement of theconvex lens assembly 20 shown in FIG. 2 is a honeycomb-shapedarrangement in which a single convex lens 21 is formed in each ofhexagonal lens forming section 22 disposed closely adjacent to eachother. The arrangement of the convex lens assembly 20 shown in FIG. 3 isa square-shaped arrangement in which a single convex lens 21 is formedin each of regular square lens forming sections 22 disposed verticallyand horizontally. The arrangement of the convex lens assembly 20 shownin FIG. 4 is a square shape in which a single convex lens 21 is formedin each of regular square pattern forming sections 22 that are arrangedvertically and horizontally at a rotational angle of 45 degrees. Thearrangement of the convex lens assembly 20 shown in FIG. 5 is a radialarrangement in which a single convex lens 21 is formed in each of lensforming sections (not shown in FIG. 5) that are disposed radially fromone point. The arrangement of the convex lens assembly 20 shown in FIG.6 is a concentric arrangement in which a single convex lens 21 is formedin each of concentrically disposed lens forming sections (not shown inFIG. 6). The arrangement of the convex lens assembly 20 shown in FIG. 7is a spiral arrangement in which a single convex lens 21 is formed ineach of lens forming sections (not shown in FIG. 7) that are disposedspirally from one point. The arrangement of the convex lens assembly 20shown in FIG. 8 is a radially curved arrangement in which the convexlenses 21 are formed within respective lens forming sections (not shownin FIG. 8) that are disposed in a curved line extending from one pointin a radial direction. In the stereoscopic sheet structure 1, which isan example of the stereoscopic sheet structure of the first embodiment,the arrangement of the lens forming sections 22 is the honeycomb-shapedarrangement shown in FIG. 2.

The convex lens 21 is preferably formed in substantially a central partof the lens forming section 22. The convex lens 21 is shaped so as to beable to focus light entering this convex lens 21. The size of the convexlens 21 may be equal to or smaller than the size of the lens formingsection and may be particularly preferably the same as that of the lensforming section. The convex lens 21 may have a thickness enough to beable to focus the light entering the convex lens 21 onto the rearsurface of the sheet member 10 and is therefore, for example,approximately 5 through 100 μm.

The convex lenses 21 are arranged toward the arrangement direction ofthe lens forming sections 22, with the arrangement intervals L betweenadjacent convex lenses 21. The length of the arrangement intervals Lbetween the convex lenses 21 at this moment is not particularlyrestricted and thus has an equal length or different lengths. In thestereoscopic sheet structure 1, which is an example of the stereoscopicsheet structure (FIG. 1), the plurality of convex lenses 21 are arrangedat the arrangement intervals L having the equal length. The length ofthe arrangement intervals L between the convex lenses 21 is preferably,for example, approximately 0.1 through 1.2 mm, and particularlypreferably 0.12 through 0.42 mm. The arrangement interval L between theconvex lenses 21 indicates the distance between any position of acertain convex lens 21 and a position of an adjacent convex lens 21 thatcorresponds to the abovementioned any position, in the arrangementdirection of the lens forming sections 22. For reference, in thearrangements shown in FIG. 2 through FIG. 8, a distance between thecenters of convex lenses 21 is illustrated as the arrangement intervalL.

The material of the convex lens assembly 20 may be one that is capableof functioning as a lens, and examples thereof include acrylic acidester resins such as acrylic acid methyl resin, methacrylic acid esterresins such as methacrylic acid methyl resin, vinyl resins, or a resincomposition having these resins.

As described above, in the stereoscopic sheet structure 1 of the firstembodiment, the surface of the sheet member 10 that does not have theconvex lens assembly 20, that is, normally the surface on which theconvex lenses formed on one of the surface of the sheet member 10 focuslight, has the repeating design portion 30. The repeating design portion3Q has a continuously deformed design portion in which the arrangementintervals and arrangement directions of the plurality of adjacent designunits 31 vary such that the arrangement of the design units 31 differsfrom that of the plurality of convex lenses 21. An example of therepeating design portion 30 of the stereoscopic sheet structure 1 isdescribed with reference to FIG. 9 through FIG. 17. It should be notedthat FIG. 9 and FIG. 14 are reference drawings for explaining thethree-dimensional moiré design of the present invention. According tothe embodiments shown in FIGS. 10, 12, 15, 16 and 17, the repeatingdesign portion 30 has the continuously deformed design portion in whichthe arrangement intervals D of the design units regularly change suchthat, when any three adjacent design units are selected, the ratio(D_(N˜N+1)/D_(N+1˜N+2)) of an interval L_(N˜N+1) between a N^(th) designunit N and a N+1^(th) design unit N+1 adjacent thereto to an intervalD_(N+1˜N+2) between the N+1^(th) design unit N+1 and a N+2^(th) designunit N+2 adjacent thereto falls within a range of 0.95 to 1.05, or, inother words, satisfies the following expression (1), and the arrangementdirection of the design units changes regularly such that anintersection angle θ (sometimes called “arrangement angle θ”hereinafter) that is formed between an extended line of a straight lineconnecting the N^(th) design unit N with the N+1^(th) design unit N+1adjacent thereto and a straight line connecting the N+1^(th) design unitN+1 with the N+2^(th) design unit N+2 adjacent thereto falls within arange of −1 degree to +1 degree, or, in other words, satisfies thefollowing expression (2).

0 95≦D _(N˜N+1) /D _(N+1˜N+2)≦1.05  Expression (1)

−1≦θ≦+1  Expression (2)

It should be noted that if the abovementioned ratio(D_(N˜N+1)/D_(N+1˜N+2)) is less than 0.95, the three-dimensional moirédesigns are so small that the degree of subduction of the designs cannotbe recognized even when the designs are observed from the convex lensassembly side, but if the abovementioned ratio is greater than 1.05 thethree-dimensional moiré patterns are so small that the degree offloating of the designs cannot be recognized even when the designs areobserved from the convex lens assembly side. Moreover, if theabovementioned intersection angle becomes less than −1 degree or exceeds+1 degree, a change in the three-dimensional moiré patterns cannot berecognized.

A repeating design that has a continuously deformed design portion 40shown in FIG. 10 can be an example of the repeating design portion 30.This continuously deformed design portion 40 is made by deforming adesign pattern 35 in which star-shaped design units 31 are arranged inan arrangement pattern similar to the arrangement of the convex lensassembly 20 (see FIG. 9), so that the arrangement interval D between twodesign units 31 adjacent in the arrangement direction of the arrangementpattern 35 and the arrangement angle θ formed by the abovementionedarrangement direction and the straight line connecting the two designunits 31 are changed continuously, as shown in FIG. 10.

As shown in FIG. 9, the design pattern 35 before deformation hasso-called similar arrangement patterns in which the arrangementdirection of the convex lenses in the convex lens assembly 20 is thesame as the arrangement direction of the design units but thearrangement interval L (referred to as “pitch”) between convex lenses isdifferent from the arrangement interval D between design units, i.e.,arrangement patterns in each of which a plurality of the star-shapeddesign units 31 are arranged at the arrangement intervals D differentfrom the arrangement intervals L between the plurality of convex lensesin the convex lens assembly 20, but the arrangement patterns of thedesign pattern 35 are not limited to such arrangement patterns.Specifically, the design pattern 35 before deformation may have anarrangement similar to the arrangement of the convex lens assembly 20,and examples include cases where the arrangement interval D of thedesign pattern 35 is smaller or larger than the arrangement interval Lof the convex lens assembly 20 and where the arrangement direction ofthe design pattern 35 is the same as or different from the arrangementdirection of the convex lens assembly 20. For example, when the convexlens assembly 20 is formed according to the arrangements shown in FIG. 2through FIG. 8, the design pattern is formed according to thearrangements shown in FIG. 2 through FIG. 8 having intervals differentfrom the arrangement intervals L in the arrangements shown in FIG. 2through FIG. 8.

Here, when a design pattern is configured by discontinuous designs, thedesign units configuring the design pattern indicate the discontinuousdesigns configuring a design pattern, and when a design pattern isconfigured by continuous designs such as a line segment, the designunits configuring the design pattern indicate divided continuous shapewhich is a part of the designs and obtained by dividing the designpattern into a lattice form at predetermined intervals. The shape of thediscontinuous designs serving as the design units is not particularlylimited, thus the examples thereof include polygons such as triangle,square, pentagon and hexagon, circle, ellipse, heart shape, star shape,tear shape, character shape, and any other shape.

Since the convex lens assembly 20 of the stereoscopic sheet structure 1(the lens forming sections 22) is formed according to thehoneycomb-shaped arrangement shown in FIG. 2, the design pattern 35 isso configured that the plurality of star-shaped design units 31 areformed according to the honeycomb-shaped arrangement, as shown in FIG.9. It should be noted that auxiliary lines X⁻⁵ through X₅ and Y⁻⁵through Y₅ shown in FIG. 9 are auxiliary lines for explaining a statefor changing the design pattern 35, and do not configure the designpattern 35.

FIG. 11 is an explanatory diagram showing regularity of the arrangementof the design units 31 in the design pattern of the first embodiment,that is, the design pattern 40 shown in, for example, FIG. 10. As shownin FIG. 11, when any three continuous design units, e.g., 31 a through31 c, of the design pattern 40 are noted, an intersection angle θ₁formed by a straight line connecting the design unit 31 a and the designunit 31 b and a straight line connecting the design unit 31 b and thedesign unit 31 c is within a range of −1 degree to +1 degree. Anintersection angle θ₂ formed by the straight line connecting the designunit 31 c and the design unit 31 b and a straight line connecting thedesign unit 31 c and a design unit 31 d is also within the range of −1degree to +1 degree. In this manner, the relationship in the expression(2) described above is satisfied in the line of the plurality of designunits. How the design pattern is designed determines the value of theangle θ within the range of −1 degree to +1 degree.

The arrangement of the design units 31 shown in FIG. 10 is so deformedthat the intersection angle θ formed by a straight line formed by twoadjacent design units and a straight line formed by another design unitsadjacent to one of the two design units in the design pattern 35 shownin FIG. 9 satisfies the abovementioned expression (1) or is continuouslyand gradually changed along the plurality of auxiliary lines x andauxiliary lines y that are arranged so that the auxiliary lines x andauxiliary lines y change the form thereof from straight lines toS-shaped curves when the design pattern 35 is designed with the view ofobtaining a visual effect.

If the arrangement angle θ of the design units 31 is changed in thismanner, as is clear from FIG. 10 and FIG. 11, the arrangement interval Dbetween the two design units 31 adjacent in the direction of anauxiliary line y₀ is also changed slightly with the abovementionedchange so as to satisfy the abovementioned expression (1), as is clearlyshown in FIG. 11. Specifically, the arrangement interval D between thetwo design units 31 adjacent in the arrangement direction along theauxiliary line y₀ continuously changes gradually or steplessly from eachof the auxiliary lines X⁻⁵ and X₅ toward the auxiliary line X₀.

The design pattern 35 shown in FIG. 9 is deformed such that thearrangement of the design units 31 along the auxiliary line x₀ and thearrangement of the design units 31 along y₀ both satisfy theabovementioned expression (1) and expression (2), and at the same timefollow the auxiliary line x₊₅ that becomes a straight line again via theS-shaped auxiliary line x₀ from the straight auxiliary line x⁻⁵ and theauxiliary line y₊₅ that becomes a straight line again via the S-shapedauxiliary line y₀ from the straight auxiliary line y⁻⁵, and such thatthe same number of design units are contained in areas surrounded by theauxiliary lines x and the auxiliary lines y, and as a result thecontinuously deformed design portion 40 is formed as shown in FIG. 10.This continuously deformed design portion 40 has an arrangement patternin which the design pattern 35 is bent or twisted at the middle wherethe auxiliary line x₀ intersects with the auxiliary line y₀.

An example of the continuously deformed design portion 40 is shown inFIG. 10 and FIG. 11, but when the arrangement angle θ shown in theexpression (2) is continuously changed the width of the arrangementangle θ and the orientation of the angle (absolute value of θ) can bearbitrarily set within a range satisfying the abovementioned expression(2).

Furthermore, as described above, in the continuously deformed designportion 40 shown in FIG. 10, the auxiliary lines x are formed such thatthe straight auxiliary line x⁻⁵ is changed again to the auxiliary linex₊₅ through the S-shaped auxiliary line x₀, and at the same time thestraight auxiliary line y⁻⁵ is changed again to the straight auxiliaryline y₊₅ through the S-shaped auxiliary line y₀, but the patterns ofchange in the auxiliary lines are not limited to such examples, thuseither the auxiliary lines x or the auxiliary line y are changedsequentially and other auxiliary lines may be kept linear or nonlinearto form the continuously deformed design portion 40 by means of aplurality of design coal arranged along these auxiliary lines.

Another example of the repeating design portion 30 includes a repeatingdesign portion (not shown) having a continuously deformed design portion41 shown in FIG. 12. The continuously deformed design portion 41 isconfigured by deforming the design pattern 35 (see FIG. 9) in which thedesign units 31 are arranged in the arrangement pattern similar to thearrangement of the convex lens assembly 20, such that the arrangementinterval D between two design units 31 adjacent in the arrangementdirection of the design pattern 35 and the arrangement angle θ formed bythe arrangement direction and the straight line connecting the twodesign units 31 change continuously.

The design pattern 35 is the same as the design pattern 35 described asan example of the repeating design portion 30, and has an arrangementpattern in which a plurality of star-shaped design units 31 are arrangedat intervals different from the arrangement intervals L of the convexlens assembly 20.

FIG. 13 is a view for explaining a continuously deformed design that isconfigured by continuously changing the arrangement interval D betweenthe two design units 31 that are adjacent in the arrangement directionfollowing the auxiliary line Y₀ in the arrangement of the design units31 formed along the auxiliary line Y₀ of the design pattern 35 shown inFIG. 9. In FIG. 13, only star-shaped design units 31 a through 31 kdisposed on the auxiliary lines X⁻⁵ through X₅ respectively areindicated by circles and deformed lines are indicated by lower-caseletters “x” and “y.”

The arrangement of the design units 31 along the y₀ shown in FIG. 12 isdeformed such that, in the design pattern 35 shown in FIG. 9, thearrangement interval D of the two design units 31 adjacent in thearrangement direction of the design pattern 35 continuously changesgradually or steplessly as shown in FIG. 13 to satisfy the relationshipof the expression (1). As a result, the arrangement of the design units31 has the intervals larger and smaller than the arrangement intervalsof the design pattern 35, and the arrangement of the design units 31between the auxiliary line x⁻⁵ and the auxiliary line x₀ and thearrangement of the design units 31 between the auxiliary line x₅ and theauxiliary line x₀ are line-symmetric to each other with respect to theauxiliary line x₀. Therefore, the arrangement interval D₁ between thedesign units 31 a and 31 b following the auxiliary line y₀ and thearrangement interval D₁ between design units 31 k and 31 j have theequal distance, and the arrangement intervals D₂ through d₅ also havethe same distances as the arrangement intervals D₂ through d₅respectively. It should be noted that FIG. 13 shows only the designunits 31 a through 31 k positioned on the auxiliary lines x⁻⁵ through x₅respectively, but the arrangement of the design units 31 along theauxiliary line Y₀ is also deformed line-symmetrically with respect tothe auxiliary line x₀.

On the other hand, the arrangement of the design units 31 along the x₀shown in FIG. 12 is also deformed line-symmetrically with respect to theauxiliary line y₀ as with the arrangement of the design units 31 athrough 31 k formed along the y₀. Specifically, the arrangement of thedesign units 31 formed along the x₀ is deformed such that, in the designpattern 35 shown in FIG. 9, the arrangement interval D of the two designunits 31 adjacent in the arrangement direction of the design pattern 35continuously changes gradually or steplessly as shown so as to satisfythe relationship of the expression (1). As a result, the arrangement ofthe design units 31 formed along the x₀ has the intervals larger andsmaller than the arrangement intervals of the design pattern 35, and allof the arrangements of the design units 31 formed along the auxiliaryline X₀ are deformed such that the arrangement of the design units 31between the auxiliary line y⁻⁵ and the auxiliary line y₀ and thearrangement of the design units 31 between the auxiliary line y₅ and theauxiliary line y₀ are line-symmetric to each other with respect to theauxiliary line y₀.

In this manner, in the design pattern 41 shown in FIG. 12, thearrangement of design units 31 formed along the auxiliary line X₀ andthe arrangement of the design units 31 formed along the auxiliary lineY₀ both are deformed line-symmetrically with respect to the auxiliaryline y₀, as described above. In the continuously deformed design portionshown in FIG. 12, the number of design units existing within a unitsection sectioned by a y-axis and an x-axis is the same in any unitsection. Furthermore, the regularity of the arrangements of the designunits in the continuously deformed design portion shown in FIG. 12 issuch that, specifically, the density of the design units existing infour unit sections around an intersection of a y₀-axis and an x₀-axis ismaximum, and such that the density of the design units within unitsections that are arranged sequentially on the outside of the four unitsections decreases toward the outside. By deforming the arrangements ofthe design units 31 in this manner, the arrangement angle θ, which isformed by the arrangement direction of the design units 31 formed alongthe auxiliary line y₀ and the straight line connecting the two designunits 31 adjacent in this arrangement direction, also slightly changeswith the deformation, such that, for example, the arrangement of thedesign units 31 formed along the auxiliary line y₄ shown in FIG. 12becomes proximate to the direction of the auxiliary line y₀, as is clearfrom FIG. 12 and FIG. 13. Specifically, in the arrangement of the designunits 31 formed along the auxiliary line y₀, the arrangement angle θ,which is formed by the arrangement direction of the arrangement of thedesign units 31 and the straight line connecting the two design units 31adjacent in this arrangement direction, is continuously changedgradually or steplessly. Such change in the arrangement angle iscommonly-observed in not only the arrangements of the design units 31formed along the auxiliary lines y but also the arrangements of thedesign units 31 formed along the auxiliary lines x. As a result, asshown in FIG. 12, the constantly deformed design portion 41 has thearrangement pattern in which the design pattern 35 converges, with theintersection of the auxiliary line X₀ and the auxiliary line Y₀ of thedesign pattern 35 at the center.

An example of the continuously deformed design portion 41 is shown inFIG. 12 and FIG. 13, but when the arrangement interval D is continuouslychanged gradually or steplessly the size of the arrangement interval Dcan be arbitrarily set as long as the abovementioned expression (1) issatisfied.

Moreover, in place of the continuously deformed design portion 41 shownin FIG. 12, for example, a continuously deformed design portion in whichone of the arrangements of the design units 31 formed along theauxiliary line y₀ and auxiliary line x₀ is deformed can be obtained.Moreover, for example, only either one of the arrangement of the designunits 31 between the auxiliary line x⁻⁵ and the auxiliary line x₀ andthe arrangement of the design units 31 between the auxiliary line X₅ andthe auxiliary line x₀ may be deformed, and the amount of change in thearrangement intervals. D in the arrangement of the design units 31between the auxiliary line x⁻⁵ and the auxiliary line x₀ and in thearrangement of the design units 31 between the auxiliary line X₅ and theauxiliary line x₀ may be set to different values to deform the botharrangements.

Another example of the repeating design portion includes a repeatingdesign portion (not shown) having a continuously deformed design portion44 shown in FIG. 15. The continuously deformed design portion 44 isconfigured by deforming a design pattern 37 (see FIG. 14) in which thestar-shaped design units 31 are arranged in the arrangement patternsimilar to the arrangement of the convex lens assembly 20, such that, asshown in FIG. 15, the arrangement interval D between two design unitsadjacent in the arrangement direction of the design pattern and thearrangement angle θ formed by this arrangement direction and thestraight line connecting the two design units change continuously.

As shown in FIG. 14, the design pattern 37 is an arrangement patternsimilar to the arrangement of the convex lens assembly 20, that is, anarrangement pattern in which a plurality of star-shaped design units 31a rearranged at arrangement intervals different from the arrangementintervals L of the convex lens assembly 20. In the design pattern 37,the plurality of star-shaped design units 31 are arranged according tothe same arrangement as the convex lens assembly 20 shown in FIG. 4,which is formed according to the square arrangement in which the convexlenses 21 are formed within the regular square lens forming sections 22that are arranged vertically and horizontally at a tilt. It should benoted that each of the auxiliary lines X⁻⁵ through X₅ and Y⁻⁵ through Y₅shown in FIG. 14 is an explanatory auxiliary line for explaining a statein which the design pattern 37 is changed, and thus is not forconfiguring the design pattern 37.

As shown in FIG. 15, as with the continuously deformed design portion40, in the continuously deformed design portion 44, the arrangements ofthe design units 31 formed along the auxiliary lines X₀ and Y₀ of thedesign pattern 37 are configured by, on the basis of the design pattern37, continuously changing the arrangement angle θ, which is formed bythe arrangement direction of the design pattern 37 and the straight lineconnecting the two design units 31 adjacent in the arrangementdirection. As a result, all of the arrangements of the design units 31formed along the auxiliary line X₀ and the auxiliary line Y₀ of thedesign pattern 37 are deformed such that the arrangement of the designunits between the auxiliary line x⁻⁵ and the auxiliary line x₀ and thearrangement of the design units between the auxiliary line x₅ and theauxiliary line x₀ are deformed from a straight-line arrangement to anS-shaped arrangement and then again to a straight-line arrangement, andthe arrangement of the design units between the auxiliary line y⁻⁵ andthe auxiliary line y₀ and the arrangement of the design units betweenthe auxiliary line y₅ and the auxiliary line y₀ are deformed from astraight-line arrangement to an S-shaped arrangement and then again to astraight-line arrangement, especially around the intersection of theauxiliary line x₀ and the auxiliary line y₀. It should be noted that inFIG. 15 the auxiliary lines obtained after the deformation are indicatedby lower-case letters “x” and “y.”

Another example of the repeating design portion includes a repeatingdesign portion having a continuously deformed design portion 45 shown inFIG. 16. The continuously deformed design portion 45 is configured bydeforming the design pattern 37 shown in FIG. 14 such that, as with thecontinuously deformed pattern portion 1, the arrangement interval Dbetween the two design units 31 adjacent in the arrangement direction ofthe design pattern 37 and the arrangement angle θ formed so as tosatisfy the expression (2) for the any three selected continuous designunits 31 change continuously. The continuously deformed design portion45 of the repeating design portion 30 shown in FIG. 16 has the intervalslarger and smaller than the arrangement intervals of the design pattern37, wherein all of the arrangements of the design units 31 along theauxiliary lines X₀ and Y₀ of the design pattern 37 are deformed suchthat the arrangement of the design units between the auxiliary line X⁻⁵and the auxiliary line x₀ and the arrangement of the design unitsbetween the auxiliary line X₅ and the auxiliary line x₀ areline-symmetric to each other with respect to the auxiliary line x₀, andsuch that the arrangement of the design units 31 between the auxiliaryline y⁻⁵ and the auxiliary line y₀ and the arrangement of the designunits 31 between the auxiliary line y₅ and the auxiliary line y₀ areline-symmetric to each other with respect to the auxiliary line y₀. Itshould be noted that in FIG. 16 the auxiliary lines obtained after thedeformation are indicated by lower-case letters “x” and “y.”

Another example of the repeating design portion includes a repeatingdesign portion 30D having a continuously deformed design portion 42 anda continuously deformed design portion 43 shown in FIG. 17. FIG. 17shows a part of the repeating design portion 30D. The repeating designportion 30D is so configured that the design units thereof deform thetwo continuously deformed design portions 42 and 43 in the x directionof the auxiliary lines and the y direction of the auxiliary lines. Itshould be noted that in FIG. 17 the line segments configuring thecontinuously deformed design portions 42 and 43 are indicated by solidlines.

As with the continuously deformed design portion 41 or 45, thecontinuously deformed design portion 42 is configured by deforming adesign pattern (not shown) composed of the design units 31. In thiscontinuously deformed design portion 42, the arrangement intervals D ofthe design units 31 change from large to small in distance around theintersection of the auxiliary line y₀ and the auxiliary line x⁻³, as thedesign unit is located farther from this intersection. The continuouslydeformed design portion 43 is configured by deforming the design pattern36 such that the arrangement intervals D of the design units 31 changefrom large to small in distance around the intersection of the auxiliaryline y₀ and the auxiliary line x₃, as the design unit is located fartherfrom this intersection, that is, by means of a deformation method thatis opposite to the one for the continuously deformed design portion 42.

The design pattern shown in FIG. 17, which is a collection of designunits, is constituted by the design pattern in which line segments arearranged in the form of a grid, i.e., vertically and horizontally, thusthe plurality of convex lenses of the convex lens assembly 20 arearranged in the form of a square in which the regular square lensforming sections shown in FIG. 3 are disposed vertically andhorizontally.

The repeating design portion having the continuously deformed designportions 40 through 45 is formed on a surface opposite to the surface ofthe sheet member 10 on which the convex lens assembly 20, that is, afocal plane of the convex lenses.

In the stereoscopic sheet structure 1, the continuously deformed designportion 40 is used as an example for describing the principle in whichthe three-dimensional moiré designs based on the repeating designportions 30, 30D having the continuously deformed design portions 40through 45 appear as though they were displaced and moved, by changingthe angle of observation, even if the visual distance is long or short.

When viewing the repeating design portion 30 having the continuouslydeformed design portion 40 through the convex lens assembly 20, thecontinuously deformed design portion 40 appears as a three-dimensionalmoiré design and as though it is displaced and moved, by changing theangle for observing it.

In the stereoscopic sheet structure 1, the three-dimensional visualeffect of the continuously deformed design portion 40 is determined bythe difference between the arrangement interval L between convex lenses21 of the convex lens assembly 20 and the arrangement interval D betweendesign units 31 of the continuously deformed design portion 40, and bythe angular difference between the arrangement direction of the convexlenses 21 of the convex lens assembly 20 and the arrangement directionof the design units 31 of the continuously deformed design portion 40.Specifically, if the arrangement interval L is larger than thearrangement interval D, the repeating design portion 30 appears asthough it were subducted, but if, on the other hand, the arrangementinterval D is larger than the arrangement interval L, the repeatingdesign portion 30 appears as though it were floating. The smaller thedifference between the arrangement interval L and the arrangementinterval D (absolute value), the larger the degree of subduction or thedegree of floating seems. Moreover, the smaller the angular differencebetween the arrangement direction of the convex lenses 21 of the convexlens assembly 20 and the arrangement direction of the design units 31 ofthe continuously deformed design portion 40 (absolute value), the largerthe degree of subduction or the degree of floating seems.

Therefore, in the continuously deformed design portion 40 in which thearrangement interval D and the arrangement angle θ in the design units31 are continuously changed gradually or steplessly, since thearrangement interval D and the arrangement angle θ of the plurality ofdesign units 31 configuring the continuously deformed design portion 40are continuously changed, the degree of subduction or degree of floatingof the continuously deformed design portion 40 also appears to bechanged continuously when viewing the continuously deformed designportion 40 via the convex lens assembly 20. As a result, thecontinuously deformed design portion 40 that appears to be subducted orfloating is enhanced three-dimensionally when viewed via the convex lensassembly 20, whereby the three-dimensional visual effect of thecontinuously deformed design portion 40 becomes significant.

On the other hand, when the angle for viewing the continuously deformeddesign portion 40 via the lens assembly 20 is changed, the degree ofmovement at which the design units 31 configuring the continuouslydeformed design portion 40 appear to be moving depends on thesignificance of the abovementioned three-dimensional visual effects.Specifically, the smaller the difference between the arrangementinterval L and the arrangement interval D (absolute value), or thesmaller the angular difference between the arrangement direction of theconvex lenses 21 of the convex lens assembly 20 and the arrangementdirection of the design units 31 of the continuously deformed designportion 40 (absolute value), the degree of subduction or degree offloating of the continuously deformed design portion increases andthereby the degree of movement of the same increases, by changing theangle for observing the continuously deformed design portion 40.Therefore, when the angle of observation is changed, the degree ofmovement at which the design units 31 configuring the continuouslydeformed design portion 40 appear to be moving is changed according tothe difference between the arrangement interval L and the arrangementinterval D (absolute value). Moreover, when the angular differencebetween the arrangement direction of the convex lenses 21 of the convexlens assembly 20 and the arrangement direction of the design units 31 ofthe continuously deformed design portion 40 (absolute value) is changed,the design units 31 configuring the continuously deformed design portion40 appear to be moving in a direction different from the direction ofmovement of eyes, when viewing from a different angle. The direction ofmovement of the design units 31 at this moment depends on the angulardifference between the arrangement direction of the convex lenses 21 ofthe convex lens assembly 20 and the arrangement direction of the designunits 31 of the continuously deformed design portion 40 (absolutevalue), thus if this difference increases, the direction of movement ofthe design units 31 diverges sharply from the direction of movement ofeyes.

As a result, in a section of the continuously deformed design portion 40in which the arrangement interval D is continuously changed, the amountof displacement of the design units 31 appears constantly differentlywhen the angle of observation is changed, and in a section in which thearrangement angle θ is continuously changed, the direction ofdisplacement of the design units 31 appears constantly differently whenthe angle of observation is changed. Therefore, when the angle forviewing the continuously deformed design portion 40 via the convex lensassembly 20 is changed, the movement of the continuously deformed designportion 40 is enhanced, whereby the continuously deformed design portionappears more clearly.

As described above, in the continuously deformed design portion 40 inwhich the difference between the arrangement interval L and thearrangement interval D (absolute value) and the angular differencebetween the arrangement direction of the convex lens 21 of the convexlens assembly 20 and the arrangement direction of the design units 31 ofthe continuously deformed design portion 40 (absolute value) arecontinuously changed gradually and steplessly, a difference iscontinuously generated in the amount of displacement of the designpattern 31 configuring the continuously deformed design portion 40 andin the direction of displacement of the design pattern 31, and, as aresult, the movement of the continuously deformed design portion 40 isenhanced to thereby appear clearly, thus the movement of thecontinuously deformed design portion 40 can be observed clearly andeasily, not only when the visual distance is short but also when thevisual distance is long.

Therefore, as in the stereoscopic sheet structure 1 of the firstembodiment according to the present invention, the three-dimensionallysubducting or floating state of the continuously deformed design portion40 viewed via the convex lens assembly 20 appears clearly, and when thecontinuously deformed design portion 40 is viewed via the lens assembly20, the three-dimensional moiré designs appear as though they weredisplaced and moved even if the visual distance is long, by changing theangle of observation.

Therefore, the stereoscopic sheet structure 1 can be applied to, forexample, a packaging material that is viewed from a short distance, and,for example, advertising display in the street, a poster, anadvertisement tower, an information display board and the like that arenormally viewed from a long distance.

In the continuously deformed design portion 40 and the continuouslydeformed design portion 44, specifically, when viewed at a differentangle via the convex lens assembly 20, the three-dimensional moirédesigns, in which the design units 31 converge toward the intersectionof the auxiliary line x₀ and the auxiliary line y₀ and float, appear asthough they flew into or flew out of the intersection.

In the continuously deformed design portion 41 and the continuouslydeformed design portion 45, specifically, when viewed at a differentangle via the convex lens assembly 20, the three-dimensional moirédesigns in which the design units 31 converge toward the intersection ofthe auxiliary line x₀ and the auxiliary line y₀ and are subducted appearas though they flew into or flew out of the intersection.

In the continuously deformed design portion 42 shown in FIG. 17,specifically, when viewed at a different angle via the convex lensassembly 20, the three-dimensional moiré designs in which the designunits 32 converge toward the intersection of the auxiliary line x⁻³ andthe auxiliary line y₀ and are subducted appear as though they flew intoor flew out of the intersection, while in the continuously deformeddesign portion 43, specifically, when viewed at a different angle viathe convex lens assembly 20, the three-dimensional moiré designs inwhich the design units 32 expand radially from the intersection of theauxiliary line x₃ and the auxiliary line y₀ and float appear as thoughthey flew into or flew out of the intersection. In other words, therepeating design portion 30D, as a whole, appears as though theundulating designs thereof having alternate convex and concave portionsrippled.

The method of producing the stereoscopic sheet structure 1 is described.First, the sheet member 10 is formed using the abovementioned materialsby a known production method such as a molding technique. At thismoment, a surface of the sheet member 10 on which the convex lens 20 isformed may be subjected to surface processing in accordance with apredetermined method to provide the abovementioned surface roughness, ormay be provided with an underlayer. The underlayer can be formed using aresin composition or the like by means of dipping, brush coating,spraying, application using a roll coater, printing, or other method.

Next, the abovementioned materials are used to form the convex lensassembly 20 on a surface of the sheet member 10. Examples of the methodfor forming the convex lens assembly 20 include a known formation methodcapable of forming the convex lens assembly 20, such as a molding methodusing a mold or a printing method.

When the sheet member 10 and the convex lens assembly 20 are formedusing the same material, the sheet member 10 and the convex lensassembly 20 may be integrally formed by means of, for example, a moldingtechnique or the like.

Next, in order to form the repeating design portion 30 having thecontinuously deformed design portion 40, first of all, in the repeatingdesign portion 30 a plurality of design units 31 are arranged usingimage editing software (for example, Adobe Illustrator™ produced byAdobe Systems, Adobe Photoshop produced by Adobe Systems, etc.) by meansof, for example, a personal computer so as to form an arrangementpattern having an arrangement interval different from the arrangementinterval L of the convex lens assembly 20, thereby creating the designpattern 35 shown in, for example FIG. 9. Next, in a partial area or theentire areas in this repeating design portion 30 (corresponding to thedesign pattern 35), the arrangement angle and arrangement interval D ofthe design pattern 35 are changed to obtain the arrangement shown inFIG. 10 by means of the abovementioned image editing software. Therepeating design portion 30 having the continuously deformed designportion 40, which is formed in the manner described above, can be formedon the surface of the sheet member 10 on which the convex lens assembly20 is not formed, that is, on the focal plane of the convex lenses,whereby the stereoscopic sheet structure 1 can be produced. It should benoted that the repeating design portion having the continuously deformeddesign portion 41 shown in FIG. 12, the continuously deformed designportion 44 shown in FIG. 15, the continuously deformed design portion 45shown in FIG. 16, and the repeating design portion 30D having thecontinuously deformed design portions 42, 42 shown in FIG. 17 can formedin the same manner.

According to the present invention, the continuously deformed designportions that are partially or entirely deformed can be easily formed asdescribed above, thus the stereoscopic sheet structure 1 can be producedeasily.

Also, the continuously deformed design portions may be configured bydeforming the design patterns by gradually or drastically changing thearrangement interval D and the arrangement angle θ of the any threecontinuous design units 31 in the arrangement direction, so long as therelationship of the expression (1) and the expression (2) are satisfiedby the abovementioned design units 31, thus the design patterns are notparticularly limited to those of the continuously deformed designportions 40 through 45.

Furthermore, each of the repeating design portions 30, 30A through 30Cin the stereoscopic sheet structure 1 has one continuously deformeddesign portion but may have two or more continuously deformed designportions as shown in FIG. 17. In this case, the two or more continuouslydeformed design portions may be the same continuously deformed designportion or different continuously deformed design portions. For example,each of the repeating design portions 30, 30A through 30C may have aplurality of the continuously deformed design portions 40 orcontinuously deformed design portions 41 or may have both in plurality.In the case in which the repeating designs have a plurality ofcontinuously deformed design portions, the continuously deformed designportions can be arranged arbitrarily.

Moreover, although it is assumed that the areas in which any of therepeating design portions 30, 30D and the continuously deformed designportions 40 through 45 in the stereoscopic sheet structure 1 are formedare square-shaped, the contour shape of the areas for forming therepeating designs and continuously deformed design portions is notparticularly limited, thus examples of the shape include polygons suchas triangle, square, pentagon and hexagon, circle, ellipse, heart shape,star shape, tear shape, arrow shape, streamline shape, character shape,and a combination of these shapes.

The configuration of the stereoscopic sheet structure according to thepresent invention is not limited to the one in which the convex lensassembly that is formed by assembling a plurality of convex lenses isformed on one surface of the transparent sheet member having one or aplurality of layers, and then the repeating design portion having thecontinuously deformed design portions is formed on the focal plane ofthe convex lenses of the sheet member. For example, as described inclaim 6 of the present application, the stereoscopic sheet structureaccording to the present invention is also a stereoscopic sheetstructure in which one surface of the first sheet member is providedwith the convex lens assembly described in claim 1, one surface of thesecond sheet member is provided with the repeating design portiondescribed in any of claims 1 through 5, and the first sheet member andthe second sheet member are stacked detachably or integrally so that thefocal plane of the convex lenses of the first sheet member faces asurface of the second sheet member that has the repeating designportion.

Specifically, in a stereoscopic sheet structure 2, as shown in FIG. 18,one surface of the first sheet member 10 has the convex lens assembly20, one surface of the second sheet member 11 has the repeating designportion 30, and the first sheet member 10 and the second sheet member 11are stacked so that the other surface of the first sheet member 10, thatis, a focal plane of the convex lenses, faces the surface of the secondsheet member 11 that has the repeating design portion 30. The sheetmember 11 in the stereoscopic sheet structure 2 may be transparent orcan be formed by means of a material such as paper, synthetic resin, acoating film or the like.

The stacked body does not have to be integrally fixed, i.e., adhered orbonded, in a state in which the sheet member 10 and the sheet member 11face each other; the sheet member 10 and the sheet member 11 may begrasped using, for example, two holding plates or the like to therebykeep the state in which the sheet member 10 and the sheet member 11 faceeach other, when the stacked body is used. In the stereoscopic sheetstructure 2 shown in FIG. 18, the repeating design portion 30 is createdand formed on a surface of the sheet member 11 by using theabovementioned method, whereby the sheet member 11 having the repeatingdesign portion 30 can be formed.

Moreover, FIG. 18 shows the stacked body having the two sheet members 10and 11, but the stacked body may have three or more stacked sheetmembers. For example, a third sheet member may be interposed between thesheet member 10 and the sheet member 11, or the sheet member 10, thesheet member 11, and the third sheet member may be stacked in thisorder. The third sheet member sometimes functions as a support layer forsupporting the sheet member 10 or the sheet member 11, and alsofunctions as a focal distance adjustment layer for adjusting the focaldistance so that the focal points of the convex lens assembly 20 form animage on the repeating designs.

In addition, the stereoscopic sheet structures 1 and 2 have therepeating designs, but may further have other designs or images inaddition to these repeating designs. For example, as in a stereoscopicsheet structure 3 shown in FIG. 19, an image 15 may be formed on asurface of the sheet member 10 on which the convex lens assembly 20 isnot formed and the repeating design portion 30 may be formed on thesurface of the image 15 as a background or the like of the image 15. Ofcourse, the repeating design portion 30 may be formed on the surface ofthe sheet member 10 and the image 15 may be formed on the surface of therepeating design portion 30.

A stereoscopic sheet structure 4 of a second embodiment of the presentinvention is described with reference to the drawings. As with thestereoscopic sheet structure 1 of the first embodiment shown in FIG. 1,in the stereoscopic sheet structure 4 shown in FIG. 20 one surface ofthe sheet member 10 has the convex lens assembly 20 on which a pluralityof lenses 21 are formed, and the other surface of the sheet member 10has repeating designs 50. The sheet member 10 and the convex lensassembly 20 of the stereoscopic sheet structure 4 according to thesecond embodiment are the same as the sheet member 10 and the convexlens assembly 20 of the stereoscopic sheet structure 1 according to thefirst embodiment. In the stereoscopic sheet structure 4 according to thesecond embodiment, for example, the convex lens assembly 20 has asquare-shaped arrangement in which the regular square lens formingsections shown in FIG. 3 are disposed vertically and horizontally.

As shown in FIG. 20, the repeating designs 50 in the stereoscopic sheetstructure 4 have a line segment assembly portion 60 in which a pluralityof line segments 65 are adjacent to one another at intervals D differentfrom the arrangement intervals L of the convex lenses 21 of the convexlens assembly 20.

The contour shape of an area forming the line segment assembly portion60 can be determined arbitrarily so as to have a desired design, and theexamples thereof include polygons such as triangle, square, pentagon andhexagon, circle, ellipse, heart shape, star shape, tear shape, arrowshape, streamline shape, character shape, and a combination of theseshapes.

The line segments 65 configuring the line segment assembly portion 60are adjacent to one another substantially parallel at intervalsdifferent from the arrangement intervals L of the convex lenses 21 ofthe convex lens assembly 20, and may be line segments capable of forminga repeating pattern, such as straight lines, curved lines, or lineshaving these lines. Examples of such line segments 65 include linesegments that extend in the same direction as the direction of extensionof the line segments that pass through convex lenses 21 adjacent to theconvex lenses 21 configuring the convex lens assembly 20. Morespecifically, the examples include, in the case in which the convex lensassembly 20 is formed according to the arrangements shown in FIG. 2,line segments that extend in the same direction as the direction ofextension of line segments 65 a through 65 c shown in FIG. 21, and inthe case in which the convex lens assembly 20 is formed according to thearrangements shown in FIG. 3, line segments that extend in the samedirection as the direction of extension of line segments 65 d through 65m shown in FIG. 22.

In the line segment assembly portion 60, the line segments thereof areassembled and adjacent to one another substantially parallel atintervals different from the arrangement intervals L of the convexlenses 21 of the convex lens assembly 20. Here, the description“intervals different from the arrangement intervals of the convex lenses21” means that, for example, the intervals between the plurality ofadjacent line segments configuring the line segment assembly portion 60are shorter than the arrangement interval L and constant, longer thanthe arrangement interval L and constant, become short or longcontinuously and gradually or drastically, and become short and longcontinuously and gradually or drastically. The abovementioned constantintervals can be, for example, 1/n through n times (n is an integerexcept 0) the arrangement interval L of the convex lenses.

In the stereoscopic sheet structure 4, each of the repeating designs 50has a star-shaped contour based on a regular hexagonal shape as shownin, for example, FIG. 23, and triangle portions obtained by dividingthis star shape into twelve triangle portions have disposed therein fourof three types of line segment assembly portions 60 a, 60 b and 60 c.The three types of line segment assembly portions 60 a, 60 b and 60 care arranged in the order of the line segment assembly portions 60 a, 60b and 60 c in a clockwise direction so that the directions of extensionof the line segments configuring these line segment assembly portions 60a through 60 c differ from the directions of extension of the linesegments configuring the two adjacent line segment assembly portions.Each of the line segments 65 configuring the line segment assemblyportions 60 a, 60 b and 60 c extends in the same direction as thedirections of extension of a line segment 65 j and of line segments 65 dand 65 f shown in FIG. 22, and the distance between adjacent linesegments 65 configuring each of the line segment assembly portions 60 a,60 b and 60 c is set to be different from the arrangement interval L ofthe convex lenses 21 configuring the convex lens assembly 20. All of thethree types of line segment assembly portions 60 a, 60 b and 60 c arearranged at a distance different from the arrangement interval L, andthe plurality of line segments 65 are arranged parallel.

As with the stereoscopic sheet structure 1, in the stereoscopic sheetstructure 4 the repeating designs 50 are formed on a convex lens focalplane, which is a surface opposite to the surface of the sheet member 10on which the convex lens assembly 20 is formed.

Hereinafter, there is described the principle in which in thestereoscopic sheet structure 4, the three-dimensional moiré designs ofthe repeating designs 50 having the line segment assembly 60 appear asthough they were displaced and moved, by changing the angle ofobservation, even if the visual distance is long or short.

When the three types of line segment assembly portions 60 a, 60 b and 60c of the repeating designs 50 are viewed via the convex lens assembly 20at a different angle, the plurality of line segments configuring each ofthe line segment assembly portions 60 a, 60 b and 60 c uniformly move inparallel, and as a result each of the line segment assembly portions 60a, 60 b and 60 c appears as though they were displaced and moved.Specifically, when the repeating design 50 shown in FIG. 23 is viewedvia the convex lens assembly 20 after moving the eyes in a horizontaldirection (lateral direction in FIG. 23), the line segment assemblyportion 60 a in which the directions of extension of the line segmentsconfiguring the line segment assembly portion match the direction ofmovement of eyes is actually displaced and moved, but the direction ofdisplacement matches the direction of movement of eyes, thus apparentlythe line segment assembly portion 60 a does not appear to be moving, butthe line segment assembly portions 60 b and 60 c in which the directionsof extension of the line segments configuring these line segmentassembly portions do not match the direction of movement of eyes appearto be moving. In this manner, a part of the repeating design 50 (linesegment assembly portion 60 a) does not appear to be moving, but otherparts (line segment assembly portions 60 b and 60 c) appear to bemoving, thus the repeating design 50 appears to be movingthree-dimensionally, when the repeating design 50 is viewed via theconvex lens assembly 20 by moving eyes in the horizontal direction.

In the repeating design 50, the plurality of line segment assemblyportions 60 a, 60 b and 60 c are disposed such that the directions ofextension of the line segments configuring a line segment assemblyportion differ from the directions of extension of the line segmentsconfiguring the two adjacent line segment assembly portions, thus, whenthe angle of observation is changed, three-dimensional movement of therepeating design 50 appears more clearly when the line segment assemblyportions move differently from one another. Therefore, according to thestereoscopic sheet structure 4 of the second embodiment of the presentinvention, when the repeating designs 50 are viewed via the lensassembly 20, even if the visual distance is long, movement of thethree-dimensional moiré designs can be viewed clearly by changing theangle for observing the repeating designs, and, when the repeatingdesign has a plurality of line segment assembly portions, movement ofthe three-dimensional moiré designs can be viewed more clearly, asdescribed above.

Therefore, the stereoscopic sheet structure 4 can be applied to, forexample, a packaging material that is usually viewed from a shortdistance, and, for example, advertising display in the street, a poster,an advertisement tower, an information display board and the like thatare normally viewed from a long distance.

When the repeating design 50 is viewed via the convex lens assembly 20by moving eyes in the horizontal direction, specifically, the linesegment assembly portion 60 a appears to be static, while the linesegment assembly portions 60 b and 60 c appear as though they wereflowing toward the outside or the inside of the repeating design 50. Onthe other hand, when viewing the repeating design 50 by moving eyes in adirection that does not match any of the directions of extension of theline segments configuring the line segment assembly portions 60 athrough 60 c, all of the line segment assembly portions 60 a through 60c appear as though they were flowing toward the outside or the inside ofthe repeating design 50 separately.

The stereoscopic sheet structure 4 can be produced in the same manner asthe stereoscopic sheet structures 1 through 3 of the first embodiment.The repeating design 50 having the line segment assembly portion 60 cancreate desired image data using the abovementioned image editingsoftware or the like using a personal computer in the same manner as,for example, the repeating design portion 30.

In the stereoscopic sheet structure 4 of the second embodiment, theshape of the repeating design 50 is not limited to a star shape havingthe line segment assembly portions 60 a through 60 c. For example, therepeating design 50 may have at least one line segment assembly portion.Furthermore, the plurality of line segments configuring the line segmentassembly portion may have intervals therebetween that continuouslybecome short gradually or steplessly, that continuously become longgradually or steplessly, and that continuously become short and longgradually or steplessly, as shown in FIG. 24. In such cases, thethree-dimensional moiré designs appear to be continuously movinggradually or steplessly. Moreover, other design or image may beinterposed between the line segments configuring the line segmentassembly portion.

Moreover, as with the stereoscopic sheet structure 1 of the firstembodiment, in the stereoscopic sheet structure 4 as well, a stackedbody of the sheet member 10 and the sheet member 11 may be provided asin the stereoscopic sheet structure 2 shown in FIG. 18, or a stackedbody in which three or more sheet members are stacked may be provided.Similarly, the stereoscopic sheet structure 4 may also be provided withother design or the image 15 besides the repeating design 50, as in thestereoscopic sheet structure 3 shown in FIG. 19.

A stereoscopic sheet structure 5 of a third embodiment of the presentinvention is described with reference to the drawings. As with thestereoscopic sheet structure 1 of the first embodiment shown in FIG. 1,in the stereoscopic sheet structure 5 shown in FIG. 25 one surface ofthe sheet member 10 has the convex lens assembly 20 on which a pluralityof lenses 21 are formed, and the other surface of the sheet member 10has repeating designs 70. The sheet member 10 and the convex lensassembly 20 of the stereoscopic sheet structure 5 according to the thirdembodiment are the same as the sheet member 10 and the convex lensassembly 20 of the stereoscopic sheet structure 1 according to the firstembodiment. In the stereoscopic sheet structure 5 according to the thirdembodiment, for example, the convex lens assembly 20 has a square-shapedarrangement in which the regular square lens forming sections shown inFIG. 3 are disposed vertically and horizontally.

As shown in FIG. 25, the repeating designs 70 of the stereoscopic sheetstructure 5 have continuously deformed design portions that areconfigured by deforming a design pattern, such that a plurality ofsections having the equal number of design units 31 are formed in thedesign pattern that has the plurality of design units 31 arranged atarrangement intervals D different from the arrangement intervals L ofthe convex lenses 21 of the convex lens assembly 20, the plurality ofsections being obtained by division at regular intervals in eacharrangement direction of the design unit 31, and the sections formedalong at least one of the arrangement directions have a plurality ofdesign units 31 arranged in the abovementioned one direction at thearrangement intervals D different from the arrangement intervalsfollowing the abovementioned one direction of the design units 31contained in at least one different section adjacent to this section inthe abovementioned direction. In other words, the repeating designs 70have continuously deformed design portions in which the design units 31are arranged, such that the plurality of design units 31 (A) arearranged at the arrangement intervals D different from the arrangementintervals L of the convex lenses 21 of the convex lens assembly 20, and(B) in sections that are obtained by division into a plurality of piecesin each arrangement direction of the design units 31 and that have theequal number of the design units 31, the arrangement intervals followingat least one of the arrangement directions of the design units 31included in one section are different from the arrangement intervalsfollowing the abovementioned one direction of the design units 31included in at least one section adjacent to this section in theabovementioned one direction. An example of the repeating designs 70 ofthe stereoscopic sheet structure 5 is described with reference to FIG.26 through FIG. 31. It should be noted that the repeating designs shownin FIG. 26 are not the repeating designs according to the presentinvention but are used as a reference for describing the repeatingdesigns according to the present invention.

Examples of the repeating designs 70 of the stereoscopic sheet structure5 of the third embodiment include repeating designs having acontinuously deformed design portion 46 shown in FIG. 27. In thiscontinuously deformed design portion 46, as shown in FIG. 27, a designpattern 38 shown in FIG. 26 is deformed such that a plurality ofsections that are obtained by division in the form of a grid at regularintervals in the vertical and horizontal arrangement directions ofdesign units 31 and have the equal number of design units 31 are formedin the design pattern in which the plurality of circular design units 31are arranged at arrangement intervals D different from the arrangementintervals L of the convex lenses 21 of the convex lens assembly 20, andthe sections that are formed along the vertical and horizontalarrangement directions of the design units 31 have the plurality ofdesign units 31 that are arranged in vertical and horizontal arrangementdirections at vertical and horizontal arrangement intervals differentfrom the vertical and horizontal arrangement intervals of the designunits 31 included in other sections adjacent to these sectionsvertically and horizontally. Specifically, as shown in FIG. 26, thecontinuously deformed design portion 46 is configured by deforming thedesign pattern 38, as described above, in which the design units 31 arearranged at an arrangement pattern similar to the arrangement of theconvex lens assembly 20.

The design pattern 38 is, specifically, an arrangement pattern havingintervals different from the arrangement intervals L of the convex lensassembly 20, as shown in FIG. 26, and the plurality of circular designunits 31 are arranged in this design pattern, but the configuration ofthe design pattern 38 is not limited to this configuration.Specifically, the design pattern 38 may be similar to the arrangement ofthe convex lens assembly 20, thus, for example, the arrangementintervals of the design pattern 38 is smaller or larger than thearrangement intervals L of the convex lens assembly 20, and thearrangement direction of the same is the same as or different from thearrangement direction in the convex lens assembly 20. For example, whenthe convex lens assembly 20 is formed according to the arrangementsshown in FIG. 2 through FIG. 8, the design patterns are formed accordingto the arrangements shown in FIG. 2 through FIG. 8 so as to have thearrangement intervals D different from the arrangement intervals L ofthe arrangements shown in FIG. 2 through FIG. 8. It should be noted thatthe design units configuring the design pattern 38 are the same as thedesign units of the stereoscopic sheet structure 1 of the firstembodiment. Since the convex lens assembly 20 (lens forming sections 22)of the stereoscopic sheet structure 5 of the third embodiment is formedaccording to the square-shaped arrangement shown in FIG. 3, in thedesign pattern 38 the plurality of circular design units 31 are formedaccording to the square-shaped arrangement, as shown in FIG. 26. Itshould be noted that the auxiliary lines X₀ through X₇ and Y₀ through Y₇shown in FIG. 26 are the explanatory auxiliary lines for explaining thestate for changing the design pattern 38 and are not for configuring thedesign pattern 38.

As shown in FIG. 26, in the design pattern 38, a plurality of grid-likesections that are obtained by division in each of the vertical andhorizontal arrangement directions of the design units 31 at regularintervals and have the equal number of design units 31 are formed. Thegrid-like sections formed in the design pattern 38 are obtained bydivision into seven pieces vertically and horizontally by the auxiliarylines X₀ through X₇ and Y₀ through Y₇ that are drawn in vertical andhorizontal arrangement directions of the design pattern 38 at regularintervals, and each of the sections has forty-nine design units 31.

The continuously deformed design portion 46 is configured by, forexample, deforming the design pattern 38 having forty-nine sectionsformed therein, as described above. In other words, in the continuouslydeformed design portion 46, the design units 31 are arranged such thatthe plurality of design units 31 (A) are arranged at the arrangementintervals D different from the arrangement intervals L of the convexlenses 21 of the convex lens assembly 20, and (B) in sections that areobtained by division in the form of a grid into a plurality of pieces inthe vertical and horizontal arrangement directions of the design units31 and that have the equal number of the design units 31, thearrangement intervals following one of the arrangement directions of thedesign units 31 included in one section are different from thearrangement intervals following the abovementioned arrangement directionof the design units 31 included in a section that is adjacent to thissection in the abovementioned arrangement direction.

Specifically, as shown in FIG. 27, in the continuously deformed designportion 46, the design pattern 38 is deformed in the direction ofextension of the auxiliary lines y and thereupon the plurality of designunits 31 are arranged, such that, for example, arrangement intervals d₁₁through d₇₁ that continue in the direction of extension of the auxiliarylines y (which may sometimes be referred to as “auxiliary line ydirection” hereinafter, and which means a horizontal arrangementdirection in the continuously deformed design portion 46 in FIG. 27) andfollow the auxiliary line y direction of the design units 31 containedin sections D₁₁ through D₇₁ respectively differ from the arrangementintervals D of the design units 31 contained in other sections adjacentto each other in the auxiliary line y direction, i.e., the arrangementintervals d₁₁ through d₇₁ in the sections D₁₁ through D₇₁ respectivelybecome small sequentially after becoming sequentially large continuouslyor non-continuously and gradually or steplessly so as to be symmetricwith respect to a section D₄₁. Specifically, the arrangement intervalsd₁₁ through d₇₁ of the design units in the sections D₁₁ through D₇₁ havea relationship of “d₁₁=d₇₁<d₂₁=d₆₁<d₃₁=d₅₁<d₄₁,” and the arrangementintervals in the auxiliary line y direction vary in the sectionsadjacent to each other in the abovementioned direction. It should benoted that the auxiliary lines x₀ through x₇ and y₀ through y₇ shown inFIG. 27 correspond to the auxiliary lines X₀ through X₇ and Y₀ throughY₇ of the design pattern 38 respectively, and are not the auxiliarylines for configuring the continuously deformed design portion 46 butare the explanatory auxiliary lines for explaining the state fordeforming the sections.

Furthermore, in the continuously deformed design portion 46, the designpattern 38 is deformed in the direction of extension of the auxiliarylines x and thereupon the plurality of design units 31 are arranged,such that, for example, arrangement intervals d₁₁ through d₁₇ thatcontinue in the direction of extension of the auxiliary lines x (whichmay sometimes be referred to as “auxiliary line x direction”hereinafter, and which means a vertical arrangement direction in thecontinuously deformed design portion 46 in FIG. 27) and follow theauxiliary line x direction of the design units 31 contained in sectionsD₁₁ through D₁₇ respectively differ from the arrangement intervals D ofthe design units 31 contained in other sections adjacent to each otherin the auxiliary line x direction at the same rate as the sections D₁₁through D₇₁ continuing in the abovementioned auxiliary line y direction,i.e., the arrangement intervals d₁₁ through d₁₇ in the sections D₁₁through D₁₇ respectively become small sequentially after becomingsequentially large continuously or non-continuously and gradually orsteplessly so as to be symmetric with respect to a section D₁₄, at thesame rate as the sections D₁₁ through D₇₁ continuing in theabovementioned auxiliary line y direction. Specifically, the arrangementintervals d₁₁ through d₁₇ of the design units in the sections D₁₁through D₁₇ have a relationship of “d₁₁=d₁₇<d₁₂=d₁₆<d₁₃=d₁₅<d₁₄,” andthe arrangement intervals in the auxiliary line x direction vary in thesections adjacent to each other in the abovementioned direction.Moreover, the arrangement intervals D in the sections formed in thecontinuously deformed design portion 46 have a relationship of“d₁₁=d₇₁=d₁₇, d₂₁=d₆₁=d₁₂=d₁₆, d₃₁=d₅₁=d₁₃=d₁₅, d₄₁=d₁₄.”

The continuously deformed design portion 46 was explained using thesections D₁₁ through D₇₁ and D₁₁ through D₁₇ as examples, but thesections continuing along the auxiliary line y direction and thesections continuing along the auxiliary line x direction are alldeformed as with the sections D₁₁ through D₇₁ and D₁₁ through D₁₇ asshown in FIG. 27, and the design units 31 are arranged similarly.

Therefore, since the continuously deformed design portion 46 is deformedsimilarly in the auxiliary line x direction and the auxiliary line ydirection and thereupon the design units 31 are arranged similarly, thusthe contour shape of the continuously deformed design portion is aregular square as with the contour shape of the design pattern 38, thedensity of the design units 31 increases toward the outside of thecontinuously deformed design portion, while the density of the designunits 31 decreases toward the inside of the continuously deformed designportion, the density of the design units 31 is the largest at thesections D₁₁, D₁₇, D₇₁ and D₇₇ located at four corners, while thedensity of the design units 31 is the smallest at the section D₄₄located at the center, and the sections arranged along a diagonal lineof the continuously deformed design portion 46 have a similar shape.

Examples of the continuously deformed design portion 46 are described inFIG. 26 and FIG. 27, but the size of the arrangement intervals d can bearbitrarily set when continuously or non-continuously changing thearrangement intervals d gradually or steplessly.

Moreover, as shown in FIG. 26, in the continuously deformed designportion 46, forty-nine sections that are obtained by dividing the designunits 31 into seven sections in each vertical and horizontal arrangementdirection at regular intervals are formed in the design pattern 38,wherein the sections that are formed along the vertical and horizontalarrangement directions of the design units 31 are arranged at verticaland horizontal arrangement intervals different from the vertical andhorizontal arrangement intervals of the design units 31 contained inother sections adjacent to these sections vertically and horizontally,so as to have the plurality of design units 31 that are arranged alongthe vertical and horizontal directions, whereby the design pattern 38 isdeformed, but the number of sections to be formed in the design pattern38 is not limited to forty-nine, and thus can be set to any number.

Moreover, in the continuously deformed design portion 46 shown in FIG.27, the design pattern 38 is deformed in the auxiliary line x directionand the auxiliary line y direction so that the arrangement interval Dbetween sections D varies, at the same rate as the auxiliary line xdirection and the auxiliary line y direction, whereby the plurality ofdesign units 31 are arranged, but the design pattern 38 may be deformedin the auxiliary line x direction and the auxiliary line y direction sothat the arrangement interval D between the sections D varies, in adifferent rate in the auxiliary line x direction and the auxiliary liney direction, whereby the plurality of design units 31 may be arranged.

In addition, in the continuously deformed design portion 46 shown inFIG. 27, the design pattern 38 is deformed in the auxiliary line xdirection and the auxiliary line y direction and thereby the pluralityof design units 31 are arranged such that the arrangement interval dbetween the sections D sequentially decreases after sequentiallyincreasing continuously or non-continuously and gradually or steplesslyand such that the intervals d become symmetric with respect to thesection D₁₄ and the section D₄₁. In the stereoscopic sheet structure 5of the third embodiment, however, the method of deformation andarrangement is not limited to such method of formation and arrangement,thus, for example, the design pattern 38 may be deformed in theauxiliary line x direction and the auxiliary line y direction andthereby the plurality of design units 31 may be arranged, such that thearrangement intervals d in the sections continuing in the auxiliary linex direction and the auxiliary line y direction sequentially become largeor small continuously or non-continuously and gradually or steplessly oralternately become large or small continuously or non-continuously andgradually or steplessly.

It should be noted that the repeating design 70 may be configured as thecontinuously deformed design portion 46 as a whole or may partially haveone or a plurality of continuously deformed design portions 46.

As another example of the repeating design 70, there is a repeatingdesign (not shown) that has a continuously deformed design portion 47shown in FIG. 28. In this continuously deformed design portion 47, asshown in FIG. 28, only the vertical arrangement direction of the designpattern 38 is deformed such that a plurality of sections that areobtained by division in the form of a grid at regular intervals in thevertical and horizontal arrangement directions of design units 31 andhave the equal number of design units 31 are formed in the designpattern in which the plurality of circular design units 31 are arrangedat arrangement intervals D different from the arrangement intervals L ofthe convex lenses 21 of the convex lens assembly 20, and the sectionsthat are formed along the vertical arrangement direction of the designunits 31 have the plurality of design units 31 that are arranged invertical arrangement direction at arrangement intervals different fromthe vertical arrangement interval of the design units 31 included inother sections adjacent to these sections. Specifically, as shown inFIG. 28, the continuously deformed design portion 47 is different fromthe continuously deformed design portion 46 in which the vertical andhorizontal arrangement directions of the design units 31 are changed, inthat only the vertical arrangement direction of the design pattern 38 isdeformed.

The continuously deformed design portion 47 is configured by deformingthe design pattern 38 having forty-nine sections formed therein, asdescribed above. In other words, in the continuously deformed designportion 47, the design units 31 are arranged such that the plurality ofdesign units 31 (A) are arranged at the arrangement intervals Ddifferent from the arrangement intervals L of the convex lenses 21 ofthe convex lens assembly 20, and (B) in sections that are obtained bydivision in the form of a grid into a plurality of pieces in thevertical and horizontal arrangement directions of the design units 31and that have the equal number of the design units 31, the arrangementintervals following the vertical arrangement direction of the designunits 31 included in one section are different from the arrangementintervals following the vertical arrangement direction of the designunits 31 included in a section that is adjacent to this section in thevertical arrangement direction.

Specifically, in the continuously deformed design portion 47, as shownin FIG. 28, the design pattern 38 is deformed in the auxiliary line xdirection and thereupon the plurality of design units 31 are arranged,such that, for example, arrangement intervals d₁₁ through d₁₇ thatcontinue in the auxiliary line x direction and follow the auxiliary linex direction of the design units 31 contained in sections D₁₁ through D₁₇respectively differ from the arrangement intervals d of the design units31 contained in other sections adjacent to each other in the auxiliaryline x direction, i.e., the arrangement intervals d₁₁ through d₁₇ in thesections D₁₁ through D₁₇ respectively become small sequentially afterbecoming sequentially large continuously or non-continuously andgradually or steplessly so as to be symmetric with respect to thesection D₁₄. Specifically, the arrangement intervals d₁₁ through d₁₇ ofthe design units in the sections D₁₁ through D₁₇ have a relationship of“d₁₁=d₁₇<d₁₂=d₁₆<d₁₃=d₁₅<d₁₄,” and the arrangement intervals in theauxiliary line x direction vary in the sections adjacent to each otherin the abovementioned direction. It should be noted that the auxiliaryline x₀ through x₁₀ and y₀ through y₇ shown in FIG. 28 are not forconfiguring the continuously deformed design portion 47, as with theauxiliary lines shown in FIG. 27.

The continuously deformed design portion 47 was explained using thesections D₁₁ through D₁₇ as examples, but the sections continuing alongthe auxiliary line x direction are all deformed as described above, asshown in FIG. 28. Also, the arrangement intervals D following theauxiliary line y direction of the design units 31 contained in thesections continuing in the auxiliary line y direction are all constantthroughout the sections, and may be the same as the arrangementintervals of the design pattern 38 or may be smaller or larger than thearrangement intervals.

Therefore, since the continuously deformed design portion 47 is deformedin the auxiliary line x direction only and there upon the design units31 are arranged, thus the continuously deformed design portion has arectangular contour shape that is different from the contour shape ofthe design pattern 38, and the density of the design units 31 increasestoward the outside in the auxiliary line x direction, while the densityof the design units 31 decreases toward the inside. As shown in FIG. 28,in the continuously deformed design portion 47, section columns D₈₁through D₈₇, section columns D₉₁ through D₉₇ and section columns D₁₀₁through D₁₀₇ are formed along an auxiliary line y-axis direction ofsection columns D₇₁ through D₇₇ continuing in the auxiliary line xdirection, so as to have a contour shape that is substantially similarto the contour shape of the design pattern 38.

The continuously deformed design portion 47 is the same as thecontinuously deformed design portion 46 in that the number of sectionsto be formed in the design patter 38 is not limited to forty-nine, thatthe arrangement intervals d to be deformed can be set arbitrarily, thatthe design pattern 38 may be deformed in the auxiliary line X directionsuch that the arrangement intervals d in the sections D continuing inthe auxiliary line x direction sequentially become large or smallcontinuously or non-continuously and gradually or steplessly, oralternately become large or small continuously or non-continuously andgradually or steplessly, and that a repeating design 70A may beconfigured as the continuously deformed design portion 47 as a whole ormay partially have one or a plurality of continuously deformed designportions 47.

As another example of the repeating design 70, there is a repeatingdesign 70B (not shown) that has a continuously deformed design portion48 shown in FIG. 29. As shown in FIG. 29, this continuously deformeddesign portion 48 is different from the continuously deformed designportion 47 in that only the vertical arrangement direction of the designpattern 38 are deformed such that the arrangement intervals D of thedesign units 31 contained in the sections formed along the verticalarrangement direction (auxiliary line x direction) of the design units31 sequentially become large after sequentially becoming smallcontinuously or non-continuously and gradually or steplessly.Specifically, in the continuously deformed design portion 48, as shownin FIG. 29, the design pattern 38 is deformed in the auxiliary line xdirection and thereupon the plurality of design units 31 are arranged,such that, for example, the arrangement intervals d₁₁ through d₁₇ thatcontinue in the auxiliary line x direction and follow the auxiliary linex direction of the design units 31 contained in the sections D₁₁ throughD₁₇ respectively differ from the arrangement intervals d of the designunits 31 contained in other sections adjacent to each other in theauxiliary line x direction, i.e., the arrangement intervals d₁₁ throughd₁₇ in the sections D₁₁ through D₁₇ respectively become largesequentially after becoming sequentially small continuously ornon-continuously and gradually or steplessly so as to be symmetric withrespect to the section D₁₄. Specifically, the arrangement intervals d₁₁through d₁₇ of the design units in the sections D₁₁ through D₁₇ have arelationship of “d₁₁=d₁₇>d₁₂=d₁₆>d₁₃=d₁₅>d₁₄.” It should be noted thatthe auxiliary line x₀ through x₅ and y₀ through y₇ shown in FIG. 29 arenot for configuring the continuously deformed design portion 48, as withthe auxiliary lines shown in FIG. 27.

The continuously deformed design portion 48 was explained using thesections D₁₁ through D₁₇ as examples, but the sections continuing alongthe auxiliary line x direction are all deformed as described above, asshown in FIG. 29. Also, the arrangement intervals d following theauxiliary line y direction of the design units 31 contained in thesections continuing in the auxiliary line y direction are all constantthroughout the sections, and may be the same as the arrangementintervals of the design pattern 38 or may be smaller or larger than thearrangement intervals.

Therefore, since the continuously deformed design portion 48 is deformedin the auxiliary line x direction only and thereupon the design units 31are arranged, thus the continuously deformed design portion has arectangular contour shape that is different from the contour shape ofthe design pattern 38, and the density of the design units 31 decreasestoward the outside in the auxiliary line x direction, while the densityof the design units 31 increases toward the inside. As shown in FIG. 29,in the continuously deformed design portion 48, section column D₆₁through D₆₇ and section columns D₇₁ through D₇₇ (all not shown) thatexist along the auxiliary line y-axis direction of section columns D₅₁through D₅₇ continuing in the auxiliary line x direction are deleted, soas to have a contour shape that is substantially similar to the contourshape of the design pattern 38.

The continuously deformed design portion 48 is the same as thecontinuously deformed design portion 46 in that the number of sectionsto be formed in the design patter 38 is not limited to forty-nine, thatthe arrangement intervals d to be deformed can be set arbitrarily, thatthe design pattern 38 may be deformed in the auxiliary line X directionsuch that the arrangement intervals d in the sections D continuing inthe auxiliary line x direction sequentially become large or smallcontinuously or non-continuously and gradually or steplessly, oralternately become large or small continuously or non-continuously andgradually or steplessly, and that the repeating design 70B may beconfigured as the continuously deformed design portion 48 as a whole ormay partially have one or a plurality of continuously deformed designportions 48.

As described above, in the continuously deformed design portion 47 andthe continuously deformed design portion 48, only the verticalarrangement direction of the design pattern 38 is deformed such that thearrangement intervals d of the design units 31 contained in the sectionsformed along the vertical arrangement direction (auxiliary line xdirection) of the design units 31 are in an opposite relationship toeach other, thus when the repeating design 70A and the repeating design70B have one continuously deformed design portion 47 and onecontinuously deformed design portion 48 respectively, the designs of therepeating design 70A and the repeating design 70B become different, butwhen the repeating design 70A and the repeating design 70B have aplurality of the continuously deformed design portions 47 and aplurality of the continuously deformed design portions 48 respectively,the repeating design 70A and the repeating design 70B have the samerepeating design.

As another example of the repeating design 70, there is a repeatingdesign 70C (not shown) that has a continuously deformed design portion49 shown in FIG. 30. As shown in FIG. 30, this continuously deformeddesign portion 49 is different from the continuously deformed designportion 46 in that the design pattern 38 is deformed in the auxiliaryline x direction and the auxiliary line y direction and thereupon theplurality of design patterns 31 are arranged, such that the arrangementintervals d of the design units 31 of the sections continuing in theauxiliary line x direction and the auxiliary line y direction aredeformed so as to become sequentially large after becoming sequentiallysmall continuously or non-continuously and gradually or steplessly.Specifically, in the continuously deformed design portion 49, the methodof deforming the design pattern 38 in the auxiliary line x direction andthe auxiliary line y direction and the arrangement intervals of thedesign units 31 are opposite to the deformation method and thearrangement intervals of the continuously deformed design portion 46.Specifically, as shown in FIG. 30, in the continuously deformed designportion 49, the design pattern 38 is deformed in the auxiliary line ydirection and thereupon the plurality of design units 31 are arrangedsuch that, for example, the arrangement intervals d₁₁ through d₇₁continuing in the auxiliary line y direction and following the auxiliaryline y direction of the design units 31 contained respectively in thesections D₁₁ through D₇₁ sequentially become small after sequentiallybecoming large continuously or non-continuously and gradually orsteplessly, and become symmetric with respect to the section D₄₁, andsuch that, for example, the arrangement intervals d₁₁ through d₁₇continuing in the auxiliary line x direction and following the auxiliaryline x direction of the design units 31 contained respectively in thesections D₁₁ through D₁₇ sequentially become small after sequentiallybecoming large continuously or non-continuously and gradually orsteplessly, and become symmetric with respect to the section D₁₄.Therefore, the arrangement intervals d₁₁ through d₇₁ of the design unitsin the sections D₁₁ through D₇₁ have a relationship of“d₁₁=d₇₁>d₂₁=d₆₁>d₃₁=d₅₁>d₄₁,” and the arrangement intervals in theauxiliary line y direction in the sections adjacent to each other in theabovementioned direction are different. Moreover, the arrangementintervals d₁₁ through d₁₇ of the design units in the sections D₁₁through D₁₇ have a relationship of “d₁₁=d₁₇>d₁₂=d₁₆>d₁₃=d₁₅>d₁₄,” andthe arrangement intervals in the auxiliary line x direction in thesections adjacent to each other in the abovementioned direction aredifferent. Furthermore, the arrangement intervals d in the sectionsformed in the continuously deformed design portion 49 have arelationship of “d₁₁=d₇₁=d₁₇, d₂₁=d₆₁=d₁₂=d₁₆, d₃₁=d₅₁ d₁₃=d₁₅, andd₄₁=d₁₄. It should be noted that the auxiliary lines x₀ through X₇ andy₀ through y₇ shown in FIG. 30 are not for configuring the continuouslydeformed design portion 49, as with the auxiliary lines shown in FIG.27.

Therefore, since the continuously deformed design portion is deformedsimilarly in the auxiliary line x direction and the auxiliary line ydirection and thereupon the design units are arranged similarly, thusthe contour shape of the continuously deformed design portion is aregular square as with the contour shape of the design pattern 38, thedensity of the design units 31 decreases toward the outside of thecontinuously deformed design portion, while the density of the designunits increases toward the inside of the continuously deformed designportion 49, the density of the design units 31 is the smallest at thesections D₁₁, D₁₇, D₇₁ and D₇₇ located at four corners, while thedensity of the design units 31 is the largest at the section D₄₄ locatedat the center, and the sections arranged along a diagonal line of thecontinuously deformed design portion 49 have a similar shape.

The continuously deformed design portion 49 is the same as thecontinuously deformed design portion 46 in that the number of sectionsto be formed in the design patter 38 is not limited to forty-nine, thatthe arrangement intervals d to be deformed can be set arbitrarily, thatthe design pattern 38 may be deformed such that the arrangementintervals d in each section D varies, in a different rate in theauxiliary line x direction and the auxiliary line y direction, that thedesign pattern 38 may be deformed in the auxiliary line x direction andthe auxiliary line y direction such that the arrangement intervals d inthe sections continuing in the auxiliary line x direction and theauxiliary line y direction sequentially become large or smallcontinuously or non-continuously and gradually or steplessly, oralternately become large or small continuously or non-continuously andgradually or steplessly, and that the repeating design 70C may beconfigured as the continuously deformed design portion 49 as a whole ormay partially have one or a plurality of continuously deformed designportions 49.

As described above, in the continuously deformed design portion 46 andthe continuously deformed design portion 49, the vertical and horizontalarrangement directions of the design pattern 38 are deformed such thatthe arrangement intervals d of the design units 31 contained in thesections formed along the vertical and horizontal arrangement directions(auxiliary line x direction and auxiliary line y direction) of thedesign units 31 are in an opposite relationship to each other, thus whenthe repeating design 70 and the repeating design 70C have onecontinuously deformed design portion 46 and one continuously deformeddesign portion 49 respectively, the designs of the repeating design 70and the repeating design 70C become different, but when the repeatingdesign 70 and the repeating design 70C have a plurality of thecontinuously deformed design portions 46 and a plurality of thecontinuously deformed design portions 49 respectively, the repeatingdesign 70 and the repeating design 70C have the same repeating design.

In the design pattern 38 of any of the continuously deformed designportions 46 through 49, there are formed a plurality of sections thatare obtained by division at regular intervals in each arrangementdirection of the design units 31 configuring the design pattern 38 andhave the equal number of design units 31, but the sections to be formedin the design pattern 38 may not necessarily be obtained by division ineach arrangement direction of the design units 31 at regular intervals,thus the sections to be formed in the design pattern may be obtained bydivision, for example, randomly in each arrangement direction, may havedifferent intervals in each arrangement direction, and may be obtainedby division at regular intervals or randomly.

Furthermore, the design pattern 38 have the design units 31 of the sameshape, but the design pattern may have a plurality of design units 31having different shapes.

It should be noted that in the design pattern 38 of any of thecontinuously deformed design portions 46 through 49, there are formed aplurality of sections that are obtained by division at regular intervalsin each arrangement direction of the design units 31 configuring thedesign pattern 38 and have the equal number of design units 31, whereinthe design pattern is deformed such that the sections that are formedalong at least one of the arrangement directions have a plurality ofdesign units that are arranged in the abovementioned one direction atarrangement intervals different from the arrangement intervals followingthe abovementioned one direction of the design units contained in othersections adjacent to these sections in the abovementioned direction.Here, the auxiliary lines for forming the abovementioned sections can beauxiliary lines that extend, for example, in two directions that areperpendicular to each other, and the arrangement intervals of the designunits 31 correspond to, for example, the length of the formed sectionsas shown in FIG. 26 through 30 (the distance between two auxiliary linesthat extend in the same direction forming the sections). Therefore, inany of the continuously deformed design portions 46 through 49, thedesign pattern 38 is deformed such that a plurality of sections D, whichare obtained by division at regular intervals in two directionsperpendicular to each other and which have the equal number of designunits 31, are formed in the design pattern that has a plurality ofdesign units 31 arranged at the arrangement intervals d different fromthe arrangement intervals L of the convex lenses 21 of the convex lensassembly 20, wherein a section D that is formed along at least one ofthe two directions perpendicular to each other has a section length thatis different from the section length of the abovementioned one directionin at least one section that is adjacent to this section D in theabovementioned at least one direction. “Two directions perpendicular toeach other” are described as follows.

As another example of the repeating design 70, there is a repeatingdesign 70D (not shown) that has a plurality of the continuously deformeddesign portion 46 shown in FIG. 31. FIG. 31 shows a part of therepeating design 70D. The repeating design 70D has a plurality of thecontinuously deformed design portions 46 that are continuously arrangedin a vertical direction and a horizontal direction.

Although the repeating design 70D has only the same continuouslydeformed design portions 46 in plurality, the repeating design may beconfigured such that different continuously deformed design portions,e.g., at least two types of continuously deformed design portions thatare selected from the group of continuously deformed design portions 46through 49, are arranged in a predetermined pattern or randomly.

Another aspect of the repeating design 70 of the stereoscopic sheetstructure 5 has a continuously deformed design portion in which a designpattern is deformed, such that a plurality of sections D, which areobtained by division at regular intervals in two directionsperpendicular to each other and have the equal number of design units31, are formed in the design pattern that has the plurality of designunits 31 arranged in arrangement intervals d different from thearrangement intervals L of the convex lenses 21 of the convex lensassembly 20, wherein a section D that is formed along at least one ofthe two directions perpendicular to other has a section length that isdifferent from the section length of the abovementioned one direction ofat least one section adjacent to this section D in the abovementioned atleast one direction. Here, “two directions perpendicular to each other”described above indicate a straight line that extends in directionpassing through one certain design pattern 31 and another design pattern31 existing around this design pattern 31 (regardless of the distancebetween the abovementioned one certain design pattern 31 and theabovementioned another design pattern 31), and a straight line that isperpendicular to this straight line.

Another aspect of the repeating design 70, specifically, has acontinuously deformed design portion in which the design units 31 arearranged such that the plurality of design units 31 (A) are arranged atthe arrangement intervals d different from the arrangement intervals Lof the convex lenses 21 of the convex lens assembly 20, and (B) in thesections that are obtained by division into a plurality of pieces in atleast one of the two directions perpendicular to each other, i.e., thevertical direction and the horizontal direction in FIG. 32, and thathave the equal number of design units 31, the section length in theabovementioned at least one direction in one section is different fromthe section length in the abovementioned at least one direction in atleast one section that is adjacent to this section in the abovementionedone direction. An example of another aspect of the repeating design 70of the stereoscopic sheet structure 5 is described with reference toFIG. 32 through FIG. 37.

As an example of another aspect of the repeating design 70 of thestereoscopic sheet structure 5 according to the third embodiment, thereis a repeating design 70E (not shown) that has a continuously deformeddesign portion 46A shown in FIG. 33. As shown in FIG. 33, in thiscontinuously deformed design portion 46A, a design pattern 39 isdeformed such that a plurality of sections D, which are obtained bydivision in the form of a grid at regular intervals in two directionsperpendicular to each other and have the equal number of design units31, are formed in the design pattern in which the plurality of circulardesign units 31 are arranged at arrangement intervals d different fromthe arrangement intervals L of the convex lenses 21 of the convex lensassembly 20, and a section D that is formed along at least one of thetwo directions perpendicular to each other has a section length that isdifferent from the section length of the abovementioned one direction inother section adjacent to this section D in the abovementioned at leastone direction. Specifically, in the continuously deformed design portion46A, the design pattern 39 in which the design units 31 are arranged inan arrangement pattern similar to the arrangement of the convex lensassembly 20 is deformed as described above as shown in FIG. 33.

As with the design pattern 38, in the design pattern 39 the plurality ofcircular design units 31 are arranged in an arrangement pattern that issimilar to the arrangement of the convex lens assembly 20, that is, inan arrangement pattern at intervals different from the arrangementintervals L of the convex lens assembly 20, as shown in FIG. 32. Morespecifically, in another aspect of the repeating design 70, since theconvex lens assembly 20 (lens forming sections 22) is formed accordingto the square-shaped arrangement rotated by 45 degrees as shown in FIG.4, the design pattern 39 is formed according to the square-shapedarrangement in which the plurality of circular design units 31 arerotated by 45 degrees, as shown in FIG. 32. Specifically, the designpattern 39 is same as the design pattern 38, except that the designpattern 38 in which the design units 31 are arranged in the form of asquare as shown in FIG. 26 is rotated by 45 degrees. It should be notedthat the auxiliary lines X₀ through X₇ and Y₀ through Y₇ shown in FIG.32 are not auxiliary lines for configuring the design pattern 39, butexplanatory auxiliary lines for explaining the state for changing thedesign pattern 39.

In the design pattern 39, there are formed a plurality of grid-likesections that are obtained by division at regular intervals in twodirections, i.e., a vertical direction (direction in which the auxiliarylines X extend) and a horizontal direction (a direction in which theauxiliary lines Y extend) in FIG. 32, and have the equal number ofdesign units 31, the two directions being perpendicular to each other atan angle of 45 degrees with respect to the arrangement direction of thedesign units 31. The grid-like sections formed in the design pattern 39are obtained by division into seven sections vertically and horizontallyby the auxiliary lines X₀ through X₇ and Y₀ through Y₇ that are drawn atregular intervals in the vertical direction and the horizontal directionof the design pattern 39, and each of the sections has forty-nine designunits 31.

The continuously deformed design portion 46A is configured by deformingthe design pattern 39 having forty-nine sections formed therein, asdescribed above. In other words, in the continuously deformed designportion 46A, the design units 31 are arranged such that the plurality ofdesign units 31 (A) are arranged at the arrangement intervals ddifferent from the arrangement intervals L of the convex lenses 21 ofthe convex lens assembly 20, and (B) in the sections that are obtainedby division into a plurality of pieces in the form of a grid in theauxiliary line X direction and the auxiliary line Y directionperpendicular to each other and that have the equal number of designunits 31, the section length in the auxiliary line X direction and theauxiliary line Y direction in one section is different from the sectionlength in the auxiliary line X direction and the auxiliary line Ydirection in a section that is adjacent to this section in the auxiliaryline X direction and the auxiliary line Y direction.

Specifically, as shown in FIG. 33, in the continuously deformed designportion 46A the design pattern 39 is deformed in an auxiliary line ydirection, such that, for example, the section length of each of thesections D₁₁ through D₇₁ (distance between two auxiliary lines extendingin the same direction for forming these sections) continuing in theauxiliary line y direction (horizontal direction of the continuouslydeformed design portion 46A in FIG. 33) differs from the section lengthof other section that is adjacent in the auxiliary line y direction,that is, the section length in the sections D₁₁ through D₇₁ sequentiallybecomes small after sequentially becoming large continuously ornon-continuously and gradually or steplessly and becomes symmetric withrespect to the section D₄₁. As a result, each arrangement interval ineach arrangement direction in the sections D₁₁ through D₇₁ sequentiallybecomes small after sequentially becoming large continuously ornon-continuously and gradually or steplessly and becomes symmetric withrespect to d₄₁, and further the angle that is formed by two arrangementdirections in the sections D₁₁ through D₇₁ changes, in accordance withthe section length deformed as described above, whereby the plurality ofdesign units 31 are arranged. It should be noted that the auxiliarylines x₀ through x₇ and y₀ through y₇ shown in FIG. 33 are not auxiliarylines for configuring the continuously deformed design portion 46A butare explanatory auxiliary lines for explaining the state for deformingthe sections in accordance with the auxiliary lines X₀ through X₇ and Y₀through Y₇ of the design pattern 39.

Furthermore, in the continuously deformed design portion 46A, the designpattern 39 is deformed in the auxiliary line y direction, such that, forexample, the section length of each of the sections D₁₁ through D₁₇continuing along the auxiliary line x direction (vertical direction ofthe continuously deformed design portion 46A in FIG. 33) changes at thesame rate as the sections D₁₁ through D₇₁ continuing in the auxiliaryline y direction, i.e., the section length in the sections D₁₁ throughD₇₁ sequentially becomes small after sequentially becoming largecontinuously or non-continuously and gradually or steplessly and becomessymmetric with respect to the section D₁₄. As a result, each arrangementinterval in each arrangement direction in the sections D₁₁ through D₁₇sequentially becomes small after sequentially becoming largecontinuously or non-continuously and gradually or steplessly and becomessymmetric with respect to d₁₄, and further the angle that is formed bytwo arrangement directions in the sections D₁₁ through D₁₇ changes, inaccordance with the section length deformed as described above, wherebythe plurality of design units 31 are arranged.

The continuously deformed design portion 46A was explained using thesections D₁₁ through D₇₁ and D₁₁ through D₁₇ as examples, but thesections continuing along the auxiliary line y direction and thesections continuing along the auxiliary line x direction are alldeformed as with the sections D₁₁ through D₇₁ and D₁₁ through D₁₇ asshown in FIG. 33, and the design units 31 are arranged similarly.

Therefore, since the continuously deformed design portion 46A isdeformed similarly in the auxiliary line x direction and the auxiliaryline y direction and thereupon the design units 31 are arrangedsimilarly, thus the contour shape of the continuously deformed designportion is a regular square as with the contour shape of the designpattern 39, the density of the design units 31 increases toward theoutside of the continuously deformed design portion, while the densityof the design units 31 decreases toward the inside of the continuouslydeformed design portion, the density of the design units 31 is thelargest at the sections D₁₁, D₁₇, D₇₁ and D₇₇ located at four corners,while the density of the design units 31 is the smallest at the sectionD₄₄ located at the center, and the sections arranged along a diagonalline of the continuously deformed design portion 46A have a similarshape.

Examples of the continuously deformed design portion 46A are describedin FIG. 32 and FIG. 33, but the size of the section length can bearbitrarily set when continuously or non-continuously changing thesection length gradually or steplessly.

Moreover, in the continuously deformed design portion 46A, forty-ninesections that are obtained by dividing the design units 31 into sevensections in the vertical direction and the horizontal direction atregular intervals are formed in the design pattern 39, and the designpattern 39 is deformed as described above, but the number of sections tobe formed in the design pattern 39 is not limited to forty-nine, andthus can be set to any number.

Moreover, in the continuously deformed design portion 46A shown in FIG.32 and FIG. 33, the design pattern 39 is deformed in the auxiliary linex direction and the auxiliary line y direction so that the sectionlength in the sections D varies, at the same rate as the auxiliary linex direction and the auxiliary line y direction, whereby the plurality ofdesign units 31 are arranged, but the design pattern 39 may be deformedin the auxiliary line x direction and the auxiliary line y direction sothat the section length in the sections D varies, in a different rate inthe auxiliary line x direction and the auxiliary line y direction,whereby the plurality of design units 31 may be arranged.

In addition, in the continuously deformed design portion 46A shown inFIG. 32 and FIG. 33, the design pattern 39 is deformed in the auxiliaryline x direction and the auxiliary line y direction and thereby theplurality of design units 31 are arranged such that the section lengthin each section D sequentially decreases after sequentially increasingcontinuously or non-continuously and gradually or steplessly and suchthat the design units become symmetric with respect to the section D₁₄and the section D₄₁, but the method of deformation and arrangement isnot limited to such method of formation and arrangement, thus, forexample, the design pattern 39 may be deformed in the auxiliary line xdirection and the auxiliary line y direction and thereby the pluralityof design units 31 may be arranged, such that the section length in thesections continuing in the auxiliary line x direction and the auxiliaryline y direction sequentially becomes large or small continuously ornon-continuously and gradually or steplessly or alternately becomeslarge or small continuously or non-continuously and gradually orsteplessly.

It should be noted that the repeating design 70E may be configured asthe continuously deformed design portion 46A as a whole or may partiallyhave one or a plurality of continuously deformed design portions 46A.

As another example of the repeating design 70 of the stereoscopic sheetstructure 5 according to the third embodiment, there is a repeatingdesign 70F (not shown) that has a continuously deformed design portion47A shown in FIG. 34. As shown in FIG. 34, in this continuously deformeddesign portion 47A, the design pattern 39 is deformed such that aplurality of sections D, which are obtained by division in the form of agrid at regular intervals in two directions perpendicular to each otherand have the equal number of design units 31, are formed in the designpattern in which the plurality of circular design units 31 are arrangedat arrangement intervals d different from the arrangement intervals L ofthe convex lenses 21 of the convex lens assembly 20, and a section Dthat is formed along the vertical direction has a section length that isdifferent from the section length of the vertical direction in othersection adjacent to this section D in the vertical direction.Specifically, the continuously deformed design portion 46A is differentfrom the continuously deformed design portion 47A in which the verticaland horizontal arrangement directions of the design units 31 aredeformed, in that only the vertical arrangement direction of the designpattern 39 is deformed.

The continuously deformed design portion 47A is configured by deformingthe design pattern 39 having forty-nine sections formed therein, asdescribed above. In other words, in the continuously deformed designportion 47A, the design units 31 are arranged such that the plurality ofdesign units 31 (A) are arranged at the arrangement intervals ddifferent from the arrangement intervals L of the convex lenses 21 ofthe convex lens assembly 20, and (B) in the sections that are obtainedby division into a plurality of pieces in the form of a grid in theauxiliary line X direction and the auxiliary line Y direction and thathave the equal number of design units 31, the section length in theauxiliary line X direction in one section is different from the sectionlength in the auxiliary line X direction in a section that is adjacentto this section in the auxiliary line X direction.

Specifically, as shown in FIG. 34, in the continuously deformed designportion 47A the design pattern 39 is deformed in the auxiliary line Xdirection, such that, as with the sections D₁₁ through D₁₇ continuingalong the auxiliary line x direction in the continuously deformed designportion 46A, for example, the section length in the sections D₁₁ throughD₁₇ continuing along the auxiliary line x direction (vertical directionof the continuously deformed design portion 47A in FIG. 34) sequentiallybecomes small after sequentially becoming large continuously ornon-continuously and gradually or steplessly and becomes symmetric withrespect to the section D₁₄. As a result, each arrangement interval ineach arrangement direction in the sections D₁₁ through D₁₇ sequentiallybecomes small after sequentially becoming large continuously ornon-continuously and gradually or steplessly and becomes symmetric withrespect to d₁₄, and further the angle that is formed by two arrangementdirections in the sections D₁₁ through D₁₇ changes, in accordance withthe section length deformed as described above, whereby the plurality ofdesign units 31 are arranged.

The continuously deformed design portion 47A was explained using thesections D₁₁ through D₁₇ as examples, but the sections continuing alongthe auxiliary line x direction are all deformed as described above, asshown in FIG. 34. Also, the section length following the auxiliary liney direction of the design units 31 contained in the sections continuingin the auxiliary line y direction is constant throughout the sections,and may be the same as the arrangement intervals of the design pattern39 or may be smaller or larger than the arrangement intervals.

Therefore, since the continuously deformed design portion 47A isdeformed in the auxiliary line x direction only and thereupon the designunits 31 are arranged, thus the continuously deformed design portion hasa rectangular contour shape that is different from the contour shape ofthe design pattern 39, and the density of the design units 31 increasestoward the outside in the auxiliary line x direction, while the densityof the design units 31 decreases toward the inside. As shown in FIG. 34,in the continuously deformed design portion 47A, section columns D₈₁through D₈₇, section columns D₉₁ through D₉₇ and section columns D₈₁through D₈₇ are formed along an auxiliary line y-axis direction ofsection columns D₇₁ through D₇₇ continuing in the auxiliary line xdirection, so as to have a contour shape that is substantially similarto the contour shape of the design pattern 39.

The continuously deformed design portion 47A is the same as thecontinuously deformed design portion 46A in that the number of sectionsto be formed in the design patter 39 is not limited to forty-nine, thatthe length of sections to be deformed can be set arbitrarily, that thedesign pattern 39 may be deformed in the auxiliary line x direction suchthat the section length in the sections continuing in the auxiliary linex direction sequentially becomes large or small continuously ornon-continuously and gradually or steplessly, or alternately becomeslarge or small continuously or non-continuously and gradually orsteplessly, and that the repeating design 70F may be configured as thecontinuously deformed design portion 46A as a whole or may partiallyhave one or a plurality of continuously deformed design portions 47A.

As an example of another aspect of the repeating design 70 of thestereoscopic sheet structure 5 according to the third embodiment, thereis a repeating design 70G (not shown) that has a continuously deformeddesign portion 48A shown in FIG. 35. The continuously deformed designportion 48A has a pattern opposite to that of the continuously deformeddesign portion 47A, that is, the continuously deformed design portion isdifferent from the continuously deformed design portion 47A in that onlythe vertical arrangement direction of the design pattern 39 is deformedsuch that the section length of the sections formed along the verticaldirection sequentially becomes large after sequentially becoming smallcontinuously or non-continuously and gradually or steplessly. As aresult, each arrangement interval in each arrangement direction in thesections D₁₁ through D₁₇ sequentially becomes small after sequentiallybecoming large continuously or non-continuously and gradually orsteplessly and becomes symmetric with respect to d₁₄, and further theangle that is formed by two arrangement directions in the sections D₁₁through D₁₇ changes, in accordance with the section length deformed asdescribed above, whereby the plurality of design units 31 are arranged.

The continuously deformed design portion 48A was explained using thesections D₁₁ through D₁₇ as examples, but the sections continuing alongthe auxiliary line x direction are all deformed as described above, asshown in FIG. 35. Also, the arrangement intervals d following theauxiliary line y direction of the design units 31 contained in thesections continuing in the auxiliary line y direction are all constantthroughout the sections, and may be the same as the arrangementintervals of the design pattern 39 or may be smaller or larger than thearrangement intervals.

Therefore, since the continuously deformed design portion 48A isdeformed in the auxiliary line x direction only and thereupon the designunits 31 are arranged, thus the continuously deformed design portion hasa rectangular contour shape that is different from the contour shape ofthe design pattern 39, and the density of the design units 31 decreasestoward the outside in the auxiliary line x direction, while the densityof the design units 31 increases toward the inside. As shown in FIG. 35,in the continuously deformed design portion 48A, section column D₆₁through D₆₇ and section columns D₇₁ through D₇₇ (all not shown) thatexist along the auxiliary line y-axis direction of section columns D₅₁through D₅₇ continuing in the auxiliary line x direction are deleted, soas to have a contour shape that is substantially similar to the contourshape of the design pattern 39.

The continuously deformed design portion 48A is the same as thecontinuously deformed design portion 47A in that the number of sectionsto be formed in the design patter 39 is not limited to forty-nine, thatthe length of sections to be deformed can be set arbitrarily, that thedesign pattern 39 may be deformed in the auxiliary line x direction suchthat the section length in the sections continuing in the auxiliary linex direction sequentially becomes large or small continuously ornon-continuously and gradually or steplessly, or alternately becomeslarge or small continuously or non-continuously and gradually orsteplessly, and that the repeating design 70G may be configured as thecontinuously deformed design portion 48A as a whole or may partiallyhave one or a plurality of continuously deformed design portions 48A.

As described above, in the continuously deformed design portion 47A andthe continuously deformed design portion 48A, the design pattern 39 isdeformed such that the section lengths of the sections formed along thevertical direction are in an opposite relationship to each other, thuswhen the repeating design 70F and the repeating design 70G have onecontinuously deformed design portion 47A and one continuously deformeddesign portion 48A respectively, the designs of the repeating design 70Fand the repeating design 70G become different, but when the repeatingdesign 70F and the repeating design 70G have a plurality of thecontinuously deformed design portions 47A and one continuously deformeddesign portions 48A respectively, the repeating design 70F and therepeating design 70G have the same repeating design.

As an example of another aspect of the repeating design 70 of thestereoscopic sheet structure 5 according to the third embodiment, thereis a repeating design 70H (not shown) that has a continuously deformeddesign portion 49A shown in FIG. 36. This continuously deformed designportion 49A is different from the continuously deformed design portion46A in that the design pattern 39 is deformed such that, as shown inFIG. 36, the section length in the sections D formed along at least oneof two directions perpendicular to each other sequentially becomeslarger after sequentially becoming small continuously ornon-continuously and gradually or steplessly. Specifically, as shown inFIG. 36, in the continuously deformed design portion 49A the method ofdeforming the design pattern 39 in the auxiliary line x direction andthe auxiliary line y direction is opposite to the deformation method ofthe continuously deformed design portion 46A. As a result, eacharrangement interval d in each arrangement direction in the sections D₁₁through D₇₁ and in the sections D₁₁ through D₁₇ sequentially becomeslarge after sequentially becoming small continuously or non-continuouslyand gradually or steplessly and becomes symmetric with respect to d₄₁and d₁₄, and further the angle that is formed by two arrangementdirections in the sections D₁₁ through D₇₁ and in the sections D₁₁through D₁₇ changes, in accordance with the section length deformed asdescribed above, whereby the plurality of design units 31 are arranged.

The continuously deformed design portion 49A was explained using thesections D₁₁ through D₇₁ and the sections D₁₁ through D₁₇ as examples,but the sections continuing along the auxiliary line y direction and thesections continuing along the auxiliary line x direction are alldeformed as with the sections D₁₁ through D₇₁ and the sections D₁₁through D₁₇, as shown in FIG. 36, whereby the design units 31 aresimilarly arranged.

Therefore, since the continuously deformed design portion 49A isdeformed similarly in the auxiliary line x direction and the auxiliaryline y direction and thereupon the design units 31 are arrangedsimilarly, thus the contour shape of the continuously deformed designportion is a regular square as with the contour shape of the designpattern 39, the density of the design units 31 decreases toward theoutside of the continuously deformed design portion, while the densityof the design units 31 increases toward the inside of the continuouslydeformed design portion, the density of the design units 31 is thesmallest at the sections D₁₁, D₁₇, D₇₁ and D₇₇ located at four corners,while the density of the design units 31 is the largest at the sectionD₄₄ located at the center, and the sections arranged along a diagonalline of the continuously deformed design portion 49A have a similarshape.

The continuously deformed design portion 49A is the same as thecontinuously deformed design portion 46A in that the number of sectionsto be formed in the design patter 39 is not limited to forty-nine, thatthe length of sections to be deformed can be set arbitrarily, that thesection length in each section D may be deformed in a different rate inthe auxiliary line x direction and the auxiliary line y direction, thatthe design pattern 39 may be deformed in the auxiliary line x directionsuch that the section length in each section D sequentially becomeslarge or small continuously or non-continuously and gradually orsteplessly, or alternately becomes large or small continuously ornon-continuously and gradually or steplessly, and that the repeatingdesign 70H may be configured as the continuously deformed design portion49A as a whole or may partially have one or a plurality of continuouslydeformed design portions 49A.

As described above, in the continuously deformed design portion 46A andthe continuously deformed design portion 49A, the design pattern 39 isdeformed such that the section lengths of the sections formed along thetwo directions perpendicular to each other are in an oppositerelationship to each other, thus when the repeating design 70E and therepeating design 70H have one continuously deformed design portion 46Aand one continuously deformed design portion 49A respectively, thedesigns of the repeating design 70E and the repeating design 70H becomedifferent, but when the repeating design 70E and the repeating design70H have a plurality of the continuously deformed design portions 46Aand one continuously deformed design portions 49A respectively, therepeating design 70E and the repeating design 70H have the samerepeating design.

In the design pattern 39 of any of the continuously deformed designportions 46A through 53, there are formed a plurality of sections thatare obtained by division at regular intervals in two directionsperpendicular to each other and have the equal number of design units31, but the sections to be formed in the design pattern 39 may notnecessarily be obtained by division at regular intervals in twodirections perpendicular to each other, thus the sections to be formedin the design pattern may be obtained by division, for example, randomlyin two directions forming a predetermined angle, may have differentintervals in the two directions forming the predetermined angle, and maybe obtained by division at regular intervals or randomly.

Furthermore, the design pattern 39 have the design units 31 of the sameshape, but the design pattern may have a plurality of design units 31having different shapes.

As an example of another aspect of the repeating design 70, there is arepeating design 70I (not shown) that has a plurality of thecontinuously deformed design portion 46A shown in FIG. 37. FIG. 37 showsa part of the repeating design 70I. The repeating design 70I has aplurality of the continuously deformed design portions 46A that arecontinuously arranged in a vertical direction and a horizontaldirection.

Although the repeating design 70I has only the same continuouslydeformed design portions 46A in plurality, the repeating design may beconfigured such that different continuously deformed design portions,e.g., at least two types of continuously deformed design portions thatare selected from the group of continuously deformed design portions 46Athrough 53, are arranged in a predetermined pattern or randomly.

In the stereoscopic sheet structure 5, the principle in which thethree-dimensional moiré designs of the repeating designs 70, 70A through70I having the continuously deformed design portions 46 through 49Aappear to be changing when the angle of observation is changed isdescribed using the continuously deformed design portion 46 as anexample.

When the repeating design 70 having the continuously deformed designportion 46 is viewed through the convex lens assembly 20, thecontinuously deformed design portion 46 as a three-dimensional designand the three-dimensional moiré design appears to be changing bygradually changing the angle of observation. As with the stereoscopicsheet structure 1, in the stereoscopic sheet structure 5, thethree-dimensional visual effect of the continuously deformed designportion 46 is determined by the difference between the arrangementinterval L between convex lenses 21 of the convex lens assembly 20 andthe arrangement interval d between design units 31 of the continuouslydeformed design portion 40. Specifically, if the arrangement interval Lis larger than the arrangement interval d, the repeating design 70appears as though it is subducted, but if, on the other hand, thearrangement interval d is larger than the arrangement interval L, therepeating design 70 appears as though it is floating. The smaller thedifference between the arrangement interval L and the arrangementinterval d (absolute value), the larger the degree of subduction or thedegree of floating seems.

Therefore, in the continuously deformed design portion 46 in which thearrangement intervals d of the design units 31 contained in thecontinuous sections are changed continuously or non-continuously andgradually or steplessly in each section, when the continuously deformeddesign portion 46 is viewed through the convex lens assembly 20, thedegree of subduction or the degree of floating of the design units 31appears to be continuously changing in each section. As a result, thestate in which the continuously deformed design portion 46 that isviewed through the convex lens assembly 20 is subducted or floating isenhanced three-dimensionally, whereby the three-dimensional visualeffect of the continuously deformed design portion 46 is improved.

On the other hand, if the angle for viewing the continuously deformeddesign portion 46 through the convex lens assembly 20 is changed fromthe top of the convex lenses 21 configuring the convex lens assembly 20to a horizontal direction, the focal point of the convex lenses 21 ischanged from the bottom of the convex lenses 21 to the horizontaldirection. Therefore, when the continuously deformed design portion 46is viewed from above the convex lenses 21, since the focal point of theconvex lenses 21 is located below the convex lenses 21, the section thatis located below the convex lenses 21 as a part of the continuouslydeformed design portion 46 appears three-dimensionally due to thedifference between the arrangement interval L and the arrangementinterval d. FIG. 38 shows the three-dimensional moiré design that can beobserved in such a state. Next, the angle of observation is moved fromthe top of the convex lenses 21 to the horizontal direction to view thecontinuously deformed design portion 46, since the focal point of theconvex lenses 21 is located to the position moved in the horizontaldirection of the convex lenses 21, the section that is a part of thecontinuously deformed design portion 46 existing in a position focusedby the convex lenses 21 appears three-dimensionally due to thedifference between the arrangement interval L and the arrangementinterval d. The three-dimensional moiré design that can be observed insuch a state is a three-dimensional moiré design different from thethree-dimensional moiré design shown in FIG. 38, since a part of thecontinuously deformed design portion 46 that has an arrangement intervaldifferent from the arrangement interval of the continuously deformeddesign portion 46 when viewing from above the convex lenses 21 is viewedthrough the convex lenses. FIG. 39 shows the three-dimensional moirédesign that can be observed in such a state.

In this manner, when the angle of observation is changed from the top ofthe convex lenses 21 configuring the convex lens assembly 20 to thehorizontal direction, the sections of the continuously deformed designportion 46 that are viewed through the convex lenses 21 vary. In thecontinuously deformed design portion 46, the design pattern 38 isdeformed in the auxiliary line x direction and the auxiliary line ydirection such that, at the same rate in the auxiliary line x directionand the auxiliary line y direction, the arrangement intervalssequentially decrease after sequentially increasing continuously ornon-continuously and gradually or steplessly and become symmetric withrespect to the section D₁₄ and the section D₄₁, thus, when the angle ofobservation is changed, the shape, size, density and the like of thedesign units contained in the sections configuring the continuouslydeformed design portion 46 observed from this angle appear differentlyaccording to the deformation of the design pattern 38. Therefore, whenthe angle for observing the continuously deformed design portion 46through the convex lens assembly 20 is changed, the three-dimensionalmoiré design appears to be changing.

In the continuously deformed design portion 46, even when the angle forobserving the continuously deformed design portion 46 through the convexlens assembly 20 is changed from the top of the convex lenses 21configuring the convex lens assembly 20 to a vertical direction, thethree-dimensional moiré design appears to be changing as with the casein which the angle for observing the continuously deformed designportion 46 through the convex lens assembly 20 from the top of theconvex lenses 21 configuring the convex lens assembly 20 to thehorizontal direction.

In this manner, when the continuously deformed design portion 46 isviewed through the convex lens assembly 20, the continuously deformeddesign portion appears to be subducted or floating three-dimensionallyclearly, and when the continuously deformed design portion 46 is viewedthrough the convex lens assembly 20 the three-dimensional moiré designappears to be changing by changing the angle of observation even if thevisual distance is long.

On the other hand, unlike the continuously deformed design portions 46through 49, in the continuously deformed design portions 46A through 49Athe arrangement intervals of the design units 31 change along with thearrangement angles of the design units 31, as described above.Therefore, compared to the continuously deformed design units 46 through49, the three-dimensional moiré designs of the continuously deformeddesign portions 46A through 53 appears more clearly.

Therefore, the stereoscopic sheet structure 5 can be applied to, forexample, a packaging material that is viewed from a short distance, and,for example, advertising display in the street, a poster, anadvertisement tower, an information display board and the like that arenormally viewed from a long distance.

In the continuously deformed design portion 47, specifically, thethree-dimensional moiré design that is the same as that of thecontinuously deformed design portion 46 can be observed only in thevertical arrangement direction of the design units 31. Also, in thecontinuously deformed design portion 48, specifically, thethree-dimensional moiré design that is opposite to that of thecontinuously deformed design portion 47 can be observed. Furthermore, inthe continuously deformed design portion 49, specifically, thethree-dimensional moiré design that is opposite to that of thecontinuously deformed design portion 46 can be observed. Moreover, inthe repeating design 70D, specifically, the three-dimensional moirédesign in which a plurality of the three-dimensional moiré designs sameas those of the continuously deformed design portion 46 are connectedcan be observed.

Moreover, in the continuously deformed design portion 46A, specifically,the three-dimensional moiré design that is the same as that of thecontinuously deformed design portion 46 can be observed, although thearrangement directions of the design units 31 are different. In thecontinuously deformed design portion 49A, specifically, thethree-dimensional moiré design that is opposite to that of thecontinuously deformed design portion 46A can be observed. In thecontinuously deformed design portion 47A, specifically, thethree-dimensional moiré design that is the same as that of thecontinuously deformed design portion 46A only in the vertical directioncan be observed. In the continuously deformed design portion 48A,specifically, the three-dimensional moiré design that is opposite tothat of the continuously deformed design portion 47A can be observed.Moreover, in the repeating design 70E, specifically, thethree-dimensional moiré design in which a plurality of thethree-dimensional moiré designs the same as those of the continuouslydeformed design portion 46A are connected can be observed.

The stereoscopic sheet structure 5 can be basically produced as with thestereoscopic sheet structures 1 through 3 of the first embodiment. Aswith the repeating design portion 30, desired image data of therepeating designs 70, 70A through 70I having the continuously deformeddesign portions 46 through 49A can be created using the image editingsoftware or the like by means of a personal computer.

As with the stereoscopic sheet structure 1 of the first embodiment, thestereoscopic sheet structure 5 may have a stacked body having two sheetmembers 10 and 11 or a stacked body in which three or more sheet membersare stacked, as in the stereoscopic sheet structure 2 shown in FIG. 18.Similarly, as with the stereoscopic sheet structure 3 shown in FIG. 19,the stereoscopic sheet structure 5 may be provided with other design orthe image 15 besides the repeating design 50.

The stereoscopic sheet structure of the present invention was describedin the first embodiment, the second embodiment, and the thirdembodiment, but the stereoscopic sheet structure of the presentinvention may be a stereoscopic sheet structure that is obtained bycombining these embodiments. For example, there may be configured astereoscopic sheet structure that has a repeating design having at leasttwo of the continuously deformed design portion of the stereoscopicsheet structure of the first embodiment, the line segment assemblyportion of the stereoscopic sheet structure of the second embodiment,and the continuously deformed design portion of the stereoscopic sheetstructure of the third embodiment. Moreover, there may be configured astereoscopic sheet structure having a repeating design that is obtainedby deforming a part or the whole of the line segment assembly portion ofthe stereoscopic sheet structure of the second embodiment, as with thecontinuously deformed design portion of the stereoscopic sheet structureof the first embodiment, such that the intervals of the line segmentsand the direction of extension of the line segments are changedcontinuously and gradually or steplessly, and/or a repeating design thatis obtained by deforming the same such that the intervals of the linesegments are changed continuously and gradually or steplessly, as withthe continuously deformed design portion of the stereoscopic sheetstructure of the third embodiment.

1. A stereoscopic sheet structure, comprising: a convex lens assemblycomprising a plurality of convex lenses provided on one surface of afirst sheet member and disposed at predetermined arrangement intervalsand in predetermined arrangement directions, wherein the convex lensesfocus light on a focal plane; and a repeating design portion in which aplurality of design units are arranged on the focal plane of the convexlenses at arrangement intervals and/or in arrangement directionsdifferent from those of the convex lenses, and which comprises a firstcontinuously deformed design portion in which the arrangement intervalsof the design units change regularly such that when any three adjacentdesign units are selected, a ratio (D_(N˜N+1)/D_(N+1˜N+2)) of aninterval D_(N˜N+1) between a N^(th) design unit N and a N+1^(th) designunit N+1 adjacent thereto to an interval D_(N+1˜N+2) between theN+1^(th) design unit N+1 and a N+2^(th) design unit N+2 adjacent theretofalls within a range from 0.95 to 1.05, and the arrangement directionsof the design units change regularly such that an intersection anglethat is formed between an extended line of a straight line connectingthe N^(th) design unit N and the N+1^(th) design unit N+1 adjacentthereto and a straight line connecting the N+1^(th) design unit N+1 andthe N+2^(th) design unit N+2 adjacent thereto falls within a range of −1degree to +1 degree.
 2. A stereoscopic sheet structure, comprising: aconvex lens assembly comprising a plurality of convex lenses provided onone surface of a first sheet member and disposed at predeterminedarrangement intervals and in predetermined arrangement directions,wherein the convex lenses focus light on a focal plane; and a repeatingdesign portion in which a plurality of design units are arranged on thefocal plane of the convex lenses at arrangement intervals and/or inarrangement directions different from those of the convex lenses, andwhich comprises a second continuously deformed design portion in which adesign pattern that has the plurality of design units arranged atarrangement intervals different from the arrangement intervals of theplurality of convex lenses of the convex lens assembly has formedtherein a plurality of sections obtained by division at regularintervals in the respective arrangement directions of the design unitsand have the equal number of design units, and the design pattern isdeformed such that the section formed along at least one of thearrangement directions has a plurality of design units that are arrangedin the one direction at arrangement intervals different from anarrangement intervals that follow the one direction in the design unitscontained in another section adjacent to the section in the onedirection.
 3. The stereoscopic sheet structure according to claim 1,wherein the repeating design portion further comprises: a secondcontinuously deformed design portion in which a design pattern that hasthe plurality of design units arranged at second arrangement intervalsdifferent from the arrangement intervals of the plurality of convexlenses of the convex lens assembly has a plurality of sections formedtherein, obtained by division at regular intervals in the respectivearrangement directions of the design units, and wherein each section hasan equal number of design units, and wherein the design pattern isdeformed such that the section formed along at least one of thearrangement directions has a plurality of design units that are arrangedin the one direction at arrangement intervals different from arrangementintervals that follow the one direction in the design units contained inanother section adjacent to the section in the one direction.
 4. Astereoscopic sheet structure comprising: a convex lens assemblycomprising a plurality of convex lenses provided on one surface of afirst sheet member and disposed at predetermined arrangement intervalsand in predetermined arrangement directions, wherein the convex lensesfocus light on a focal plane; and a repeating design portion in which aplurality of design units are arranged on the focal plane of the convexlenses at arrangement intervals and/or in arrangement directionsdifferent from those of the convex lenses, and which has a line segmentassembly portion in which the design units are line segments, and theplurality of line segments are arranged at intervals different from thearrangement intervals of the convex lenses of the convex lens assembly.5. The stereoscopic sheet structure according to claim 4, wherein therepeating design portion has a plurality of the line segment assemblyportions, and directions of extension of the plurality of line segmentsforming one of the line segment assembly portions are different fromdirections of extension of the line segments forming other line segmentassembly portions.
 6. The stereoscopic sheet structure according toclaim 1, wherein the focal plane is on one surface of a second sheetmember, and the first sheet member and the second sheet member arestacked detachably or integrally.
 7. The stereoscopic sheet structureaccording to claim 2, wherein the focal plane is on one surface of asecond sheet member, and the first sheet member and the second sheetmember are stacked detachably or integrally.
 8. The stereoscopic sheetstructure according to claim 3, wherein the focal plane is on onesurface of a second sheet member, and the first sheet member and thesecond sheet member are stacked detachably or integrally.
 9. Thestereoscopic sheet structure according to claim 4, wherein the focalplane is on one surface of a second sheet member, and the first sheetmember and the second sheet member are stacked detachably or integrally.10. The stereoscopic sheet structure according to claim 5, wherein thefocal plane is on one surface of a second sheet member, and the firstsheet member and the second sheet member are stacked detachably orintegrally.
 11. The stereoscopic sheet structure according to claim 1,wherein the focal plane is on the other surface of the first sheetmember.
 12. The stereoscopic sheet structure according to claim 2,wherein the focal plane is on the other surface of the first sheetmember.
 13. The stereoscopic sheet structure according to claim 3,wherein the focal plane is on the other surface of the first sheetmember.
 14. The stereoscopic sheet structure according to claim 4,wherein the focal plane is on the other surface of the first sheetmember.
 15. The stereoscopic sheet structure according to claim 5,wherein the focal plane is on the other surface of the first sheetmember.